diff --git a/404.html b/404.html
index 86b062ef..6a7834ec 100644
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diff --git a/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js b/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js
deleted file mode 100644
index 39956173..00000000
--- a/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js
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Coba salah satu pencarian berikut ini:",searching:"Mencari [SEARCH_TERM]..."},_a={thanks_to:er,comments:ur,direction:tr,strings:rr},sr={};F(sr,{comments:()=>lr,default:()=>ca,direction:()=>nr,strings:()=>ir,thanks_to:()=>ar});var ar="Cosette Bruhns Alonso, Andrew Janco <apjanco@upenn.edu>",lr="",nr="ltr",ir={placeholder:"Cerca",clear_search:"Cancella la cronologia",load_more:"Mostra più risultati",search_label:"Cerca nel sito",filters_label:"Filtri di ricerca",zero_results:"Nessun risultato per [SEARCH_TERM]",many_results:"[COUNT] risultati per [SEARCH_TERM]",one_result:"[COUNT] risultato per [SEARCH_TERM]",alt_search:"Nessun risultato per [SEARCH_TERM]. Mostrando risultati per [DIFFERENT_TERM] come alternativa.",search_suggestion:"Nessun risultato per [SEARCH_TERM]. 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[DIFFERENT_TERM]에 대한 결과",search_suggestion:"[SEARCH_TERM]에 대한 결과 없음. 추천 검색어: ",searching:"[SEARCH_TERM] 검색 중..."},Ea={thanks_to:hr,comments:mr,direction:Cr,strings:gr},Ar={};F(Ar,{comments:()=>Br,default:()=>da,direction:()=>pr,strings:()=>vr,thanks_to:()=>Rr});var Rr="",Br="",pr="ltr",vr={placeholder:"Rapu",clear_search:"Whakakore",load_more:"Whakauta ētahi otinga kē",search_label:"Rapu",filters_label:"Tātari",zero_results:"Otinga kore ki [SEARCH_TERM]",many_results:"[COUNT] otinga ki [SEARCH_TERM]",one_result:"[COUNT] otinga ki [SEARCH_TERM]",alt_search:"Otinga kore ki [SEARCH_TERM]. Otinga kē ki [DIFFERENT_TERM]",search_suggestion:"Otinga kore ki [SEARCH_TERM]. whakamātau ki ngā mea atu:",searching:"Rapu ki [SEARCH_TERM]..."},da={thanks_to:Rr,comments:Br,direction:pr,strings:vr},Tr={};F(Tr,{comments:()=>kr,default:()=>ha,direction:()=>br,strings:()=>Dr,thanks_to:()=>Fr});var Fr="Paul van Brouwershaven",kr="",br="ltr",Dr={placeholder:"Zoeken",clear_search:"Reset",load_more:"Meer resultaten laden",search_label:"Doorzoek deze site",filters_label:"Filters",zero_results:"Geen resultaten voor [SEARCH_TERM]",many_results:"[COUNT] resultaten voor [SEARCH_TERM]",one_result:"[COUNT] resultaat voor [SEARCH_TERM]",alt_search:"Geen resultaten voor [SEARCH_TERM]. In plaats daarvan worden resultaten voor [DIFFERENT_TERM] weergegeven",search_suggestion:"Geen resultaten voor [SEARCH_TERM]. Probeer een van de volgende zoekopdrachten:",searching:"Zoeken naar [SEARCH_TERM]..."},ha={thanks_to:Fr,comments:kr,direction:br,strings:Dr},Mr={};F(Mr,{comments:()=>Hr,default:()=>ma,direction:()=>yr,strings:()=>wr,thanks_to:()=>Sr});var Sr="Christopher Wingate",Hr="",yr="ltr",wr={placeholder:"Søk",clear_search:"Fjern",load_more:"Last flere resultater",search_label:"Søk på denne siden",filters_label:"Filtre",zero_results:"Ingen resultater for [SEARCH_TERM]",many_results:"[COUNT] resultater for [SEARCH_TERM]",one_result:"[COUNT] resultat for [SEARCH_TERM]",alt_search:"Ingen resultater for [SEARCH_TERM]. Viser resultater for [DIFFERENT_TERM] i stedet",search_suggestion:"Ingen resultater for [SEARCH_TERM]. Prøv en av disse søkeordene i stedet:",searching:"Søker etter [SEARCH_TERM]"},ma={thanks_to:Sr,comments:Hr,direction:yr,strings:wr},Nr={};F(Nr,{comments:()=>jr,default:()=>Ca,direction:()=>Or,strings:()=>Ur,thanks_to:()=>zr});var zr="",jr="",Or="ltr",Ur={placeholder:"Szukaj",clear_search:"Wyczyść",load_more:"Załaduj więcej",search_label:"Przeszukaj tę stronę",filters_label:"Filtry",zero_results:"Brak wyników dla [SEARCH_TERM]",many_results:"[COUNT] wyników dla [SEARCH_TERM]",one_result:"[COUNT] wynik dla [SEARCH_TERM]",alt_search:"Brak wyników dla [SEARCH_TERM]. Wyświetlam wyniki dla [DIFFERENT_TERM]",search_suggestion:"Brak wyników dla [SEARCH_TERM]. Pokrewne wyniki wyszukiwania:",searching:"Szukam [SEARCH_TERM]..."},Ca={thanks_to:zr,comments:jr,direction:Or,strings:Ur},Ir={};F(Ir,{comments:()=>Lr,default:()=>ga,direction:()=>xr,strings:()=>qr,thanks_to:()=>Pr});var Pr="Jonatah",Lr="",xr="ltr",qr={placeholder:"Pesquisar",clear_search:"Limpar",load_more:"Ver mais resultados",search_label:"Pesquisar",filters_label:"Filtros",zero_results:"Nenhum resultado encontrado para [SEARCH_TERM]",many_results:"[COUNT] resultados encontrados para [SEARCH_TERM]",one_result:"[COUNT] resultado encontrado para [SEARCH_TERM]",alt_search:"Nenhum resultado encontrado para [SEARCH_TERM]. Exibindo resultados para [DIFFERENT_TERM]",search_suggestion:"Nenhum resultado encontrado para [SEARCH_TERM]. Tente uma das seguintes pesquisas:",searching:"Pesquisando por [SEARCH_TERM]..."},ga={thanks_to:Pr,comments:Lr,direction:xr,strings:qr},Vr={};F(Vr,{comments:()=>Gr,default:()=>Aa,direction:()=>Jr,strings:()=>Wr,thanks_to:()=>Kr});var Kr="Bogdan Mateescu <bogdan@surfverse.com>",Gr="",Jr="ltr",Wr={placeholder:"Căutare",clear_search:"Ştergeţi",load_more:"Încărcați mai multe rezultate",search_label:"Căutați în acest site",filters_label:"Filtre",zero_results:"Niciun rezultat pentru [SEARCH_TERM]",many_results:"[COUNT] rezultate pentru [SEARCH_TERM]",one_result:"[COUNT] rezultat pentru [SEARCH_TERM]",alt_search:"Niciun rezultat pentru [SEARCH_TERM]. Se afișează în schimb rezultatele pentru [DIFFERENT_TERM]",search_suggestion:"Niciun rezultat pentru [SEARCH_TERM]. Încercați una dintre următoarele căutări:",searching:"Se caută după: [SEARCH_TERM]..."},Aa={thanks_to:Kr,comments:Gr,direction:Jr,strings:Wr},Zr={};F(Zr,{comments:()=>Xr,default:()=>Ra,direction:()=>Qr,strings:()=>$r,thanks_to:()=>Yr});var Yr="Aleksandr Gordeev",Xr="",Qr="ltr",$r={placeholder:"Поиск",clear_search:"Очистить поле",load_more:"Загрузить еще",search_label:"Поиск по сайту",filters_label:"Фильтры",zero_results:"Ничего не найдено по запросу: [SEARCH_TERM]",many_results:"[COUNT] результатов по запросу: [SEARCH_TERM]",one_result:"[COUNT] результат по запросу: [SEARCH_TERM]",alt_search:"Ничего не найдено по запросу: [SEARCH_TERM]. Показаны результаты по запросу: [DIFFERENT_TERM]",search_suggestion:"Ничего не найдено по запросу: [SEARCH_TERM]. Попробуйте один из следующих вариантов",searching:"Поиск по запросу: [SEARCH_TERM]"},Ra={thanks_to:Yr,comments:Xr,direction:Qr,strings:$r},es={};F(es,{comments:()=>ts,default:()=>Ba,direction:()=>rs,strings:()=>ss,thanks_to:()=>us});var us="Andrija Sagicc",ts="",rs="ltr",ss={placeholder:"Претрага",clear_search:"Брисање",load_more:"Приказ више резултата",search_label:"Претрага сајта",filters_label:"Филтери",zero_results:"Нема резултата за [SEARCH_TERM]",many_results:"[COUNT] резултата за [SEARCH_TERM]",one_result:"[COUNT] резултата за [SEARCH_TERM]",alt_search:"Нема резултата за [SEARCH_TERM]. Приказ додатник резултата за [DIFFERENT_TERM]",search_suggestion:"Нема резултата за [SEARCH_TERM]. Покушајте са неком од следећих претрага:",searching:"Претрага термина [SEARCH_TERM]..."},Ba={thanks_to:us,comments:ts,direction:rs,strings:ss},as={};F(as,{comments:()=>ns,default:()=>pa,direction:()=>is,strings:()=>os,thanks_to:()=>ls});var ls="Montazar Al-Jaber <montazar@nanawee.tech>",ns="",is="ltr",os={placeholder:"Sök",clear_search:"Rensa",load_more:"Visa fler träffar",search_label:"Sök på denna sida",filters_label:"Filter",zero_results:"[SEARCH_TERM] gav inga träffar",many_results:"[SEARCH_TERM] gav [COUNT] träffar",one_result:"[SEARCH_TERM] gav [COUNT] träff",alt_search:"[SEARCH_TERM] gav inga träffar. Visar resultat för [DIFFERENT_TERM] istället",search_suggestion:"[SEARCH_TERM] gav inga träffar. Försök igen med en av följande sökord:",searching:"Söker efter [SEARCH_TERM]..."},pa={thanks_to:ls,comments:ns,direction:is,strings:os},_s={};F(_s,{comments:()=>fs,default:()=>va,direction:()=>Es,strings:()=>ds,thanks_to:()=>cs});var cs="Anonymous",fs="",Es="ltr",ds={placeholder:"Tafuta",clear_search:"Futa",load_more:"Pakia matokeo zaidi",search_label:"Tafuta tovuti hii",filters_label:"Vichujio",zero_results:"Hakuna matokeo ya [SEARCH_TERM]",many_results:"Matokeo [COUNT] ya [SEARCH_TERM]",one_result:"Tokeo [COUNT] la [SEARCH_TERM]",alt_search:"Hakuna mayokeo ya [SEARCH_TERM]. Badala yake, inaonyesha matokeo ya [DIFFERENT_TERM]",search_suggestion:"Hakuna matokeo ya [SEARCH_TERM]. Jaribu mojawapo ya utafutaji ufuatao:",searching:"Kutafuta [SEARCH_TERM]..."},va={thanks_to:cs,comments:fs,direction:Es,strings:ds},hs={};F(hs,{comments:()=>Cs,default:()=>Ta,direction:()=>gs,strings:()=>As,thanks_to:()=>ms});var ms="",Cs="",gs="ltr",As={placeholder:"தேடுக",clear_search:"அழிக்குக",load_more:"மேலும் முடிவுகளைக் காட்டுக",search_label:"இந்த தளத்தில் தேடுக",filters_label:"வடிகட்டல்கள்",zero_results:"[SEARCH_TERM] க்கான முடிவுகள் இல்லை",many_results:"[SEARCH_TERM] க்கான [COUNT] முடிவுகள்",one_result:"[SEARCH_TERM] க்கான முடிவு",alt_search:"[SEARCH_TERM] இத்தேடலுக்கான முடிவுகள் இல்லை, இந்த தேடல்களுக்கான ஒத்த முடிவுகள் [DIFFERENT_TERM]",search_suggestion:"[SEARCH_TERM] இத் தேடலுக்கான முடிவுகள் இல்லை.இதற்கு பதிலீடான தேடல்களை தேடுக:",searching:"[SEARCH_TERM] தேடப்படுகின்றது"},Ta={thanks_to:ms,comments:Cs,direction:gs,strings:As},Rs={};F(Rs,{comments:()=>ps,default:()=>Fa,direction:()=>vs,strings:()=>Ts,thanks_to:()=>Bs});var Bs="Taylan Özgür Bildik",ps="",vs="ltr",Ts={placeholder:"Araştır",clear_search:"Temizle",load_more:"Daha fazla sonuç",search_label:"Site genelinde arama",filters_label:"Filtreler",zero_results:"[SEARCH_TERM] için sonuç yok",many_results:"[SEARCH_TERM] için [COUNT] sonuç bulundu",one_result:"[SEARCH_TERM] için [COUNT] sonuç bulundu",alt_search:"[SEARCH_TERM] için sonuç yok. Bunun yerine [DIFFERENT_TERM] için sonuçlar gösteriliyor",search_suggestion:"[SEARCH_TERM] için sonuç yok. Alternatif olarak aşağıdaki kelimelerden birini deneyebilirsiniz:",searching:"[SEARCH_TERM] araştırılıyor..."},Fa={thanks_to:Bs,comments:ps,direction:vs,strings:Ts},Fs={};F(Fs,{comments:()=>bs,default:()=>ka,direction:()=>Ds,strings:()=>Ms,thanks_to:()=>ks});var ks="Vladyslav Lyshenko <vladdnepr1989@gmail.com>",bs="",Ds="ltr",Ms={placeholder:"Пошук",clear_search:"Очистити поле",load_more:"Завантажити ще",search_label:"Пошук по сайту",filters_label:"Фільтри",zero_results:"Нічого не знайдено за запитом: [SEARCH_TERM]",many_results:"[COUNT] результатів на запит: [SEARCH_TERM]",one_result:"[COUNT] результат за запитом: [SEARCH_TERM]",alt_search:"Нічого не знайдено на запит: [SEARCH_TERM]. Показано результати на запит: [DIFFERENT_TERM]",search_suggestion:"Нічого не знайдено на запит: [SEARCH_TERM]. 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[SEARCH_TERM] 的相關結果",one_result:"找到 [COUNT] 個 [SEARCH_TERM] 的相關結果",alt_search:"未找到 [SEARCH_TERM] 的相關結果。改為顯示 [DIFFERENT_TERM] 的相關結果",search_suggestion:"未找到 [SEARCH_TERM] 的相關結果。請嘗試以下搜索。",searching:"正在搜索 [SEARCH_TERM]..."},Ma={thanks_to:Ls,comments:xs,direction:qs,strings:Vs},Ks={};F(Ks,{comments:()=>Js,default:()=>Sa,direction:()=>Ws,strings:()=>Zs,thanks_to:()=>Gs});var Gs="Amber Song",Js="",Ws="ltr",Zs={placeholder:"搜索",clear_search:"清除",load_more:"加载更多结果",search_label:"站内搜索",filters_label:"筛选",zero_results:"未找到 [SEARCH_TERM] 的相关结果",many_results:"找到 [COUNT] 个 [SEARCH_TERM] 的相关结果",one_result:"找到 [COUNT] 个 [SEARCH_TERM] 的相关结果",alt_search:"未找到 [SEARCH_TERM] 的相关结果。改为显示 [DIFFERENT_TERM] 的相关结果",search_suggestion:"未找到 [SEARCH_TERM] 的相关结果。请尝试以下搜索。",searching:"正在搜索 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Související výsledky hledání:",searching:"Hledám [SEARCH_TERM]..."},X0={thanks_to:qu,comments:Vu,direction:Ku,strings:Gu},Ju={};F(Ju,{comments:()=>Zu,default:()=>Q0,direction:()=>Yu,strings:()=>Xu,thanks_to:()=>Wu});var Wu="Jonas Smedegaard <dr@jones.dk>",Zu="",Yu="ltr",Xu={placeholder:"Søg",clear_search:"Nulstil",load_more:"Indlæs flere resultater",search_label:"Søg på dette website",filters_label:"Filtre",zero_results:"Ingen resultater for [SEARCH_TERM]",many_results:"[COUNT] resultater for [SEARCH_TERM]",one_result:"[COUNT] resultat for [SEARCH_TERM]",alt_search:"Ingen resultater for [SEARCH_TERM]. Viser resultater for [DIFFERENT_TERM] i stedet",search_suggestion:"Ingen resultater for [SEARCH_TERM]. Prøv et af disse søgeord i stedet:",searching:"Søger efter [SEARCH_TERM]..."},Q0={thanks_to:Wu,comments:Zu,direction:Yu,strings:Xu},Qu={};F(Qu,{comments:()=>et,default:()=>$0,direction:()=>ut,strings:()=>tt,thanks_to:()=>$u});var $u="Jan Claasen <jan@cloudcannon.com>",et="",ut="ltr",tt={placeholder:"Suche",clear_search:"Löschen",load_more:"Mehr Ergebnisse laden",search_label:"Suche diese Seite",filters_label:"Filter",zero_results:"Keine Ergebnisse für [SEARCH_TERM]",many_results:"[COUNT] Ergebnisse für [SEARCH_TERM]",one_result:"[COUNT] Ergebnis für [SEARCH_TERM]",alt_search:"Keine Ergebnisse für [SEARCH_TERM]. Stattdessen werden Ergebnisse für [DIFFERENT_TERM] angezeigt",search_suggestion:"Keine Ergebnisse für [SEARCH_TERM]. Versuchen Sie eine der folgenden Suchen:",searching:"Suche für [SEARCH_TERM]"},$0={thanks_to:$u,comments:et,direction:ut,strings:tt},rt={};F(rt,{comments:()=>at,default:()=>ea,direction:()=>lt,strings:()=>nt,thanks_to:()=>st});var st="Liam Bigelow <liam@cloudcannon.com>",at="",lt="ltr",nt={placeholder:"Search",clear_search:"Clear",load_more:"Load more results",search_label:"Search this site",filters_label:"Filters",zero_results:"No results for [SEARCH_TERM]",many_results:"[COUNT] results for [SEARCH_TERM]",one_result:"[COUNT] result for [SEARCH_TERM]",alt_search:"No results for [SEARCH_TERM]. Showing results for [DIFFERENT_TERM] instead",search_suggestion:"No results for [SEARCH_TERM]. Try one of the following searches:",searching:"Searching for [SEARCH_TERM]..."},ea={thanks_to:st,comments:at,direction:lt,strings:nt},it={};F(it,{comments:()=>_t,default:()=>ua,direction:()=>ct,strings:()=>ft,thanks_to:()=>ot});var ot="Pablo Villaverde <https://github.com/pvillaverde>",_t="",ct="ltr",ft={placeholder:"Buscar",clear_search:"Limpiar",load_more:"Ver más resultados",search_label:"Buscar en este sitio",filters_label:"Filtros",zero_results:"No se encontraron resultados para [SEARCH_TERM]",many_results:"[COUNT] resultados encontrados para [SEARCH_TERM]",one_result:"[COUNT] resultado encontrado para [SEARCH_TERM]",alt_search:"No se encontraron resultados para [SEARCH_TERM]. Mostrando en su lugar resultados para [DIFFERENT_TERM]",search_suggestion:"No se encontraron resultados para [SEARCH_TERM]. Prueba una de las siguientes búsquedas:",searching:"Buscando [SEARCH_TERM]..."},ua={thanks_to:ot,comments:_t,direction:ct,strings:ft},Et={};F(Et,{comments:()=>ht,default:()=>ta,direction:()=>mt,strings:()=>Ct,thanks_to:()=>dt});var dt="Ali Khaleqi Yekta <https://yekta.dev>",ht="",mt="rtl",Ct={placeholder:"جستجو",clear_search:"پاکسازی",load_more:"بارگذاری نتایج بیشتر",search_label:"جستجو در سایت",filters_label:"فیلترها",zero_results:"نتیجه‌ای برای [SEARCH_TERM] یافت نشد",many_results:"[COUNT] نتیجه برای [SEARCH_TERM] یافت شد",one_result:"[COUNT] نتیجه برای [SEARCH_TERM] یافت شد",alt_search:"نتیجه‌ای برای [SEARCH_TERM] یافت نشد. در عوض نتایج برای [DIFFERENT_TERM] نمایش داده می‌شود",search_suggestion:"نتیجه‌ای برای [SEARCH_TERM] یافت نشد. یکی از جستجوهای زیر را امتحان کنید:",searching:"در حال جستجوی [SEARCH_TERM]..."},ta={thanks_to:dt,comments:ht,direction:mt,strings:Ct},gt={};F(gt,{comments:()=>Rt,default:()=>ra,direction:()=>Bt,strings:()=>pt,thanks_to:()=>At});var At="Valtteri Laitinen <dev@valtlai.fi>",Rt="",Bt="ltr",pt={placeholder:"Haku",clear_search:"Tyhjennä",load_more:"Lataa lisää tuloksia",search_label:"Hae tältä sivustolta",filters_label:"Suodattimet",zero_results:"Ei tuloksia haulle [SEARCH_TERM]",many_results:"[COUNT] tulosta haulle [SEARCH_TERM]",one_result:"[COUNT] tulos haulle [SEARCH_TERM]",alt_search:"Ei tuloksia haulle [SEARCH_TERM]. Näytetään tulokset sen sijaan haulle [DIFFERENT_TERM]",search_suggestion:"Ei tuloksia haulle [SEARCH_TERM]. Kokeile jotain seuraavista:",searching:"Haetaan [SEARCH_TERM]..."},ra={thanks_to:At,comments:Rt,direction:Bt,strings:pt},vt={};F(vt,{comments:()=>Ft,default:()=>sa,direction:()=>kt,strings:()=>bt,thanks_to:()=>Tt});var Tt="Nicolas Friedli <nicolas@theologique.ch>",Ft="",kt="ltr",bt={placeholder:"Rechercher",clear_search:"Nettoyer",load_more:"Charger plus de résultats",search_label:"Recherche sur ce site",filters_label:"Filtres",zero_results:"Pas de résultat pour [SEARCH_TERM]",many_results:"[COUNT] résultats pour [SEARCH_TERM]",one_result:"[COUNT] résultat pour [SEARCH_TERM]",alt_search:"Pas de résultat pour [SEARCH_TERM]. Montre les résultats pour [DIFFERENT_TERM] à la place",search_suggestion:"Pas de résultat pour [SEARCH_TERM]. Essayer une des recherches suivantes:",searching:"Recherche [SEARCH_TERM]..."},sa={thanks_to:Tt,comments:Ft,direction:kt,strings:bt},Dt={};F(Dt,{comments:()=>St,default:()=>aa,direction:()=>Ht,strings:()=>wt,thanks_to:()=>Mt});var Mt="Pablo Villaverde <https://github.com/pvillaverde>",St="",Ht="ltr",wt={placeholder:"Buscar",clear_search:"Limpar",load_more:"Ver máis resultados",search_label:"Buscar neste sitio",filters_label:"Filtros",zero_results:"Non se atoparon resultados para [SEARCH_TERM]",many_results:"[COUNT] resultados atopados para [SEARCH_TERM]",one_result:"[COUNT] resultado atopado para [SEARCH_TERM]",alt_search:"Non se atoparon resultados para [SEARCH_TERM]. Amosando no seu lugar resultados para [DIFFERENT_TERM]",search_suggestion:"Non se atoparon resultados para [SEARCH_TERM]. Probe unha das seguintes pesquisas:",searching:"Buscando [SEARCH_TERM]..."},aa={thanks_to:Mt,comments:St,direction:Ht,strings:wt},yt={};F(yt,{comments:()=>zt,default:()=>la,direction:()=>jt,strings:()=>Ot,thanks_to:()=>Nt});var Nt="Nir Tamir <nirtamir2@gmail.com>",zt="",jt="rtl",Ot={placeholder:"חיפוש",clear_search:"ניקוי",load_more:"עוד תוצאות",search_label:"חיפוש באתר זה",filters_label:"מסננים",zero_results:"לא נמצאו תוצאות עבור [SEARCH_TERM]",many_results:"נמצאו [COUNT] תוצאות עבור [SEARCH_TERM]",one_result:"נמצאה תוצאה אחת עבור [SEARCH_TERM]",alt_search:"לא נמצאו תוצאות עבור [SEARCH_TERM]. מוצגות תוצאות עבור [DIFFERENT_TERM]",search_suggestion:"לא נמצאו תוצאות עבור [SEARCH_TERM]. נסו אחד מהחיפושים הבאים:",searching:"מחפש את [SEARCH_TERM]..."},la={thanks_to:Nt,comments:zt,direction:jt,strings:Ot},Ut={};F(Ut,{comments:()=>Pt,default:()=>na,direction:()=>Lt,strings:()=>xt,thanks_to:()=>It});var It="Amit Yadav <amit@thetechbasket.com>",Pt="",Lt="ltr",xt={placeholder:"खोजें",clear_search:"साफ करें",load_more:"और अधिक परिणाम लोड करें",search_label:"इस साइट में खोजें",filters_label:"फ़िल्टर",zero_results:"कोई परिणाम [SEARCH_TERM] के लिए नहीं मिला",many_results:"[COUNT] परिणाम [SEARCH_TERM] के लिए मिले",one_result:"[COUNT] परिणाम [SEARCH_TERM] के लिए मिला",alt_search:"[SEARCH_TERM] के लिए कोई परिणाम नहीं मिला। इसके बजाय [DIFFERENT_TERM] के लिए परिणाम दिखा रहा है",search_suggestion:"[SEARCH_TERM] के लिए कोई परिणाम नहीं मिला। निम्नलिखित खोजों में से कोई एक आज़माएं:",searching:"[SEARCH_TERM] की खोज की जा रही है..."},na={thanks_to:It,comments:Pt,direction:Lt,strings:xt},qt={};F(qt,{comments:()=>Kt,default:()=>ia,direction:()=>Gt,strings:()=>Jt,thanks_to:()=>Vt});var Vt="Diomed <https://github.com/diomed>",Kt="",Gt="ltr",Jt={placeholder:"Traži",clear_search:"Očisti",load_more:"Učitaj više rezultata",search_label:"Pretraži ovu stranicu",filters_label:"Filteri",zero_results:"Nema rezultata za [SEARCH_TERM]",many_results:"[COUNT] rezultata za [SEARCH_TERM]",one_result:"[COUNT] rezultat za [SEARCH_TERM]",alt_search:"Nema rezultata za [SEARCH_TERM]. Prikazujem rezultate za [DIFFERENT_TERM]",search_suggestion:"Nema rezultata za [SEARCH_TERM]. Pokušaj s jednom od ovih pretraga:",searching:"Pretražujem [SEARCH_TERM]..."},ia={thanks_to:Vt,comments:Kt,direction:Gt,strings:Jt},Wt={};F(Wt,{comments:()=>Yt,default:()=>oa,direction:()=>Xt,strings:()=>Qt,thanks_to:()=>Zt});var Zt="Adam Laki <info@adamlaki.com>",Yt="",Xt="ltr",Qt={placeholder:"Keresés",clear_search:"Törlés",load_more:"További találatok betöltése",search_label:"Keresés az oldalon",filters_label:"Szűrés",zero_results:"Nincs találat a(z) [SEARCH_TERM] kifejezésre",many_results:"[COUNT] db találat a(z) [SEARCH_TERM] kifejezésre",one_result:"[COUNT] db találat a(z) [SEARCH_TERM] kifejezésre",alt_search:"Nincs találat a(z) [SEARCH_TERM] kifejezésre. Találatok mutatása inkább a(z) [DIFFERENT_TERM] kifejezésre",search_suggestion:"Nincs találat a(z) [SEARCH_TERM] kifejezésre. Próbáld meg a következő keresések egyikét:",searching:"Keresés a(z) [SEARCH_TERM] kifejezésre..."},oa={thanks_to:Zt,comments:Yt,direction:Xt,strings:Qt},$t={};F($t,{comments:()=>ur,default:()=>_a,direction:()=>tr,strings:()=>rr,thanks_to:()=>er});var er="Nixentric",ur="",tr="ltr",rr={placeholder:"Cari",clear_search:"Bersihkan",load_more:"Muat lebih banyak hasil",search_label:"Telusuri situs ini",filters_label:"Filter",zero_results:"[SEARCH_TERM] tidak ditemukan",many_results:"Ditemukan [COUNT] hasil untuk [SEARCH_TERM]",one_result:"Ditemukan [COUNT] hasil untuk [SEARCH_TERM]",alt_search:"[SEARCH_TERM] tidak ditemukan. Menampilkan hasil [DIFFERENT_TERM] sebagai gantinya",search_suggestion:"[SEARCH_TERM] tidak ditemukan. Coba salah satu pencarian berikut ini:",searching:"Mencari [SEARCH_TERM]..."},_a={thanks_to:er,comments:ur,direction:tr,strings:rr},sr={};F(sr,{comments:()=>lr,default:()=>ca,direction:()=>nr,strings:()=>ir,thanks_to:()=>ar});var ar="Cosette Bruhns Alonso, Andrew Janco <apjanco@upenn.edu>",lr="",nr="ltr",ir={placeholder:"Cerca",clear_search:"Cancella la cronologia",load_more:"Mostra più risultati",search_label:"Cerca nel sito",filters_label:"Filtri di ricerca",zero_results:"Nessun risultato per [SEARCH_TERM]",many_results:"[COUNT] risultati per [SEARCH_TERM]",one_result:"[COUNT] risultato per [SEARCH_TERM]",alt_search:"Nessun risultato per [SEARCH_TERM]. Mostrando risultati per [DIFFERENT_TERM] come alternativa.",search_suggestion:"Nessun risultato per [SEARCH_TERM]. Prova una delle seguenti ricerche:",searching:"Cercando [SEARCH_TERM]..."},ca={thanks_to:ar,comments:lr,direction:nr,strings:ir},or={};F(or,{comments:()=>cr,default:()=>fa,direction:()=>fr,strings:()=>Er,thanks_to:()=>_r});var _r="Tate",cr="",fr="ltr",Er={placeholder:"検索",clear_search:"クリア",load_more:"次を読み込む",search_label:"このサイトを検索",filters_label:"フィルタ",zero_results:"[SEARCH_TERM]の検索に一致する情報はありませんでした",many_results:"[SEARCH_TERM]の[COUNT]件の検索結果",one_result:"[SEARCH_TERM]の[COUNT]件の検索結果",alt_search:"[SEARCH_TERM]の検索に一致する情報はありませんでした。[DIFFERENT_TERM]の検索結果を表示しています",search_suggestion:"[SEARCH_TERM]の検索に一致する情報はありませんでした。次のいずれかの検索を試してください",searching:"[SEARCH_TERM]を検索しています"},fa={thanks_to:_r,comments:cr,direction:fr,strings:Er},dr={};F(dr,{comments:()=>mr,default:()=>Ea,direction:()=>Cr,strings:()=>gr,thanks_to:()=>hr});var hr="Seokho Son <https://github.com/seokho-son>",mr="",Cr="ltr",gr={placeholder:"검색어",clear_search:"비우기",load_more:"검색 결과 더 보기",search_label:"사이트 검색",filters_label:"필터",zero_results:"[SEARCH_TERM]에 대한 결과 없음",many_results:"[SEARCH_TERM]에 대한 결과 [COUNT]건",one_result:"[SEARCH_TERM]에 대한 결과 [COUNT]건",alt_search:"[SEARCH_TERM]에 대한 결과 없음. [DIFFERENT_TERM]에 대한 결과",search_suggestion:"[SEARCH_TERM]에 대한 결과 없음. 추천 검색어: ",searching:"[SEARCH_TERM] 검색 중..."},Ea={thanks_to:hr,comments:mr,direction:Cr,strings:gr},Ar={};F(Ar,{comments:()=>Br,default:()=>da,direction:()=>pr,strings:()=>vr,thanks_to:()=>Rr});var Rr="",Br="",pr="ltr",vr={placeholder:"Rapu",clear_search:"Whakakore",load_more:"Whakauta ētahi otinga kē",search_label:"Rapu",filters_label:"Tātari",zero_results:"Otinga kore ki [SEARCH_TERM]",many_results:"[COUNT] otinga ki [SEARCH_TERM]",one_result:"[COUNT] otinga ki [SEARCH_TERM]",alt_search:"Otinga kore ki [SEARCH_TERM]. Otinga kē ki [DIFFERENT_TERM]",search_suggestion:"Otinga kore ki [SEARCH_TERM]. whakamātau ki ngā mea atu:",searching:"Rapu ki [SEARCH_TERM]..."},da={thanks_to:Rr,comments:Br,direction:pr,strings:vr},Tr={};F(Tr,{comments:()=>kr,default:()=>ha,direction:()=>br,strings:()=>Dr,thanks_to:()=>Fr});var Fr="Paul van Brouwershaven",kr="",br="ltr",Dr={placeholder:"Zoeken",clear_search:"Reset",load_more:"Meer resultaten laden",search_label:"Doorzoek deze site",filters_label:"Filters",zero_results:"Geen resultaten voor [SEARCH_TERM]",many_results:"[COUNT] resultaten voor [SEARCH_TERM]",one_result:"[COUNT] resultaat voor [SEARCH_TERM]",alt_search:"Geen resultaten voor [SEARCH_TERM]. In plaats daarvan worden resultaten voor [DIFFERENT_TERM] weergegeven",search_suggestion:"Geen resultaten voor [SEARCH_TERM]. Probeer een van de volgende zoekopdrachten:",searching:"Zoeken naar [SEARCH_TERM]..."},ha={thanks_to:Fr,comments:kr,direction:br,strings:Dr},Mr={};F(Mr,{comments:()=>Hr,default:()=>ma,direction:()=>wr,strings:()=>yr,thanks_to:()=>Sr});var Sr="Christopher Wingate",Hr="",wr="ltr",yr={placeholder:"Søk",clear_search:"Fjern",load_more:"Last flere resultater",search_label:"Søk på denne siden",filters_label:"Filtre",zero_results:"Ingen resultater for [SEARCH_TERM]",many_results:"[COUNT] resultater for [SEARCH_TERM]",one_result:"[COUNT] resultat for [SEARCH_TERM]",alt_search:"Ingen resultater for [SEARCH_TERM]. Viser resultater for [DIFFERENT_TERM] i stedet",search_suggestion:"Ingen resultater for [SEARCH_TERM]. Prøv en av disse søkeordene i stedet:",searching:"Søker etter [SEARCH_TERM]"},ma={thanks_to:Sr,comments:Hr,direction:wr,strings:yr},Nr={};F(Nr,{comments:()=>jr,default:()=>Ca,direction:()=>Or,strings:()=>Ur,thanks_to:()=>zr});var zr="",jr="",Or="ltr",Ur={placeholder:"Szukaj",clear_search:"Wyczyść",load_more:"Załaduj więcej",search_label:"Przeszukaj tę stronę",filters_label:"Filtry",zero_results:"Brak wyników dla [SEARCH_TERM]",many_results:"[COUNT] wyników dla [SEARCH_TERM]",one_result:"[COUNT] wynik dla [SEARCH_TERM]",alt_search:"Brak wyników dla [SEARCH_TERM]. Wyświetlam wyniki dla [DIFFERENT_TERM]",search_suggestion:"Brak wyników dla [SEARCH_TERM]. Pokrewne wyniki wyszukiwania:",searching:"Szukam [SEARCH_TERM]..."},Ca={thanks_to:zr,comments:jr,direction:Or,strings:Ur},Ir={};F(Ir,{comments:()=>Lr,default:()=>ga,direction:()=>xr,strings:()=>qr,thanks_to:()=>Pr});var Pr="Jonatah",Lr="",xr="ltr",qr={placeholder:"Pesquisar",clear_search:"Limpar",load_more:"Ver mais resultados",search_label:"Pesquisar",filters_label:"Filtros",zero_results:"Nenhum resultado encontrado para [SEARCH_TERM]",many_results:"[COUNT] resultados encontrados para [SEARCH_TERM]",one_result:"[COUNT] resultado encontrado para [SEARCH_TERM]",alt_search:"Nenhum resultado encontrado para [SEARCH_TERM]. Exibindo resultados para [DIFFERENT_TERM]",search_suggestion:"Nenhum resultado encontrado para [SEARCH_TERM]. Tente uma das seguintes pesquisas:",searching:"Pesquisando por [SEARCH_TERM]..."},ga={thanks_to:Pr,comments:Lr,direction:xr,strings:qr},Vr={};F(Vr,{comments:()=>Gr,default:()=>Aa,direction:()=>Jr,strings:()=>Wr,thanks_to:()=>Kr});var Kr="Bogdan Mateescu <bogdan@surfverse.com>",Gr="",Jr="ltr",Wr={placeholder:"Căutare",clear_search:"Ştergeţi",load_more:"Încărcați mai multe rezultate",search_label:"Căutați în acest site",filters_label:"Filtre",zero_results:"Niciun rezultat pentru [SEARCH_TERM]",many_results:"[COUNT] rezultate pentru [SEARCH_TERM]",one_result:"[COUNT] rezultat pentru [SEARCH_TERM]",alt_search:"Niciun rezultat pentru [SEARCH_TERM]. Se afișează în schimb rezultatele pentru [DIFFERENT_TERM]",search_suggestion:"Niciun rezultat pentru [SEARCH_TERM]. Încercați una dintre următoarele căutări:",searching:"Se caută după: [SEARCH_TERM]..."},Aa={thanks_to:Kr,comments:Gr,direction:Jr,strings:Wr},Zr={};F(Zr,{comments:()=>Xr,default:()=>Ra,direction:()=>Qr,strings:()=>$r,thanks_to:()=>Yr});var Yr="Aleksandr Gordeev",Xr="",Qr="ltr",$r={placeholder:"Поиск",clear_search:"Очистить поле",load_more:"Загрузить еще",search_label:"Поиск по сайту",filters_label:"Фильтры",zero_results:"Ничего не найдено по запросу: [SEARCH_TERM]",many_results:"[COUNT] результатов по запросу: [SEARCH_TERM]",one_result:"[COUNT] результат по запросу: [SEARCH_TERM]",alt_search:"Ничего не найдено по запросу: [SEARCH_TERM]. Показаны результаты по запросу: [DIFFERENT_TERM]",search_suggestion:"Ничего не найдено по запросу: [SEARCH_TERM]. Попробуйте один из следующих вариантов",searching:"Поиск по запросу: [SEARCH_TERM]"},Ra={thanks_to:Yr,comments:Xr,direction:Qr,strings:$r},es={};F(es,{comments:()=>ts,default:()=>Ba,direction:()=>rs,strings:()=>ss,thanks_to:()=>us});var us="Andrija Sagicc",ts="",rs="ltr",ss={placeholder:"Претрага",clear_search:"Брисање",load_more:"Приказ више резултата",search_label:"Претрага сајта",filters_label:"Филтери",zero_results:"Нема резултата за [SEARCH_TERM]",many_results:"[COUNT] резултата за [SEARCH_TERM]",one_result:"[COUNT] резултата за [SEARCH_TERM]",alt_search:"Нема резултата за [SEARCH_TERM]. Приказ додатник резултата за [DIFFERENT_TERM]",search_suggestion:"Нема резултата за [SEARCH_TERM]. Покушајте са неком од следећих претрага:",searching:"Претрага термина [SEARCH_TERM]..."},Ba={thanks_to:us,comments:ts,direction:rs,strings:ss},as={};F(as,{comments:()=>ns,default:()=>pa,direction:()=>is,strings:()=>os,thanks_to:()=>ls});var ls="Montazar Al-Jaber <montazar@nanawee.tech>",ns="",is="ltr",os={placeholder:"Sök",clear_search:"Rensa",load_more:"Visa fler träffar",search_label:"Sök på denna sida",filters_label:"Filter",zero_results:"[SEARCH_TERM] gav inga träffar",many_results:"[SEARCH_TERM] gav [COUNT] träffar",one_result:"[SEARCH_TERM] gav [COUNT] träff",alt_search:"[SEARCH_TERM] gav inga träffar. Visar resultat för [DIFFERENT_TERM] istället",search_suggestion:"[SEARCH_TERM] gav inga träffar. Försök igen med en av följande sökord:",searching:"Söker efter [SEARCH_TERM]..."},pa={thanks_to:ls,comments:ns,direction:is,strings:os},_s={};F(_s,{comments:()=>fs,default:()=>va,direction:()=>Es,strings:()=>ds,thanks_to:()=>cs});var cs="Anonymous",fs="",Es="ltr",ds={placeholder:"Tafuta",clear_search:"Futa",load_more:"Pakia matokeo zaidi",search_label:"Tafuta tovuti hii",filters_label:"Vichujio",zero_results:"Hakuna matokeo ya [SEARCH_TERM]",many_results:"Matokeo [COUNT] ya [SEARCH_TERM]",one_result:"Tokeo [COUNT] la [SEARCH_TERM]",alt_search:"Hakuna mayokeo ya [SEARCH_TERM]. Badala yake, inaonyesha matokeo ya [DIFFERENT_TERM]",search_suggestion:"Hakuna matokeo ya [SEARCH_TERM]. 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diff --git a/_astro/_subject_.CbuzD2Qq.css b/_astro/_subject_.CbuzD2Qq.css
deleted file mode 100644
index cd8f2d2d..00000000
--- a/_astro/_subject_.CbuzD2Qq.css
+++ /dev/null
@@ -1 +0,0 @@
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index c0f3c5df..00000000
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diff --git a/_astro/index.CxbSBppY.css b/_astro/index.CxbSBppY.css
new file mode 100644
index 00000000..aa530fea
--- /dev/null
+++ b/_astro/index.CxbSBppY.css
@@ -0,0 +1 @@
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@@ -375,7 +375,7 @@ <h3 id="sorting--searching">Sorting &#x26; Searching</h3>
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-<p>This concludes this part, next time I’ll write about (short) about Complexity - after that the major part of this course, actual data structures and how we use them as well as implement them.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/chalmers/dat038/dat038_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Complexity (1) </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>This concludes this part, next time I’ll write about (short) about Complexity - after that the major part of this course, actual data structures and how we use them as well as implement them.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/chalmers/dat038/dat038_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Complexity (1) </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -547,7 +547,7 @@ <h4 id="amortised-complexity">Amortised Complexity:</h4>
 <p>For example, we use this to make dynamic arrays have an amortised complexity of $\mathcal{O}(1)$.</p>
 <p>However, when we’re calculating the total runtime of a program, it’s safe to forget about this amortised bit and just treat each operation as costing $\mathcal{O}(1)$.</p>
 <h3 id="conclusion">Conclusion</h3>
-<p>This was it for this part - and the final part in this series. I really enjoyed this DSA course, super fun :).</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat038/dat038_9" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Shortest Path &amp; Spanning Trees </div> </a> <div class="invisible"></div> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>This was it for this part - and the final part in this series. I really enjoyed this DSA course, super fun :).</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat038/dat038_9" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Shortest Path &amp; Spanning Trees </div> </a> <div class="invisible"></div> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -350,7 +350,7 @@ <h3 id="relatives-of-o-notation">Relatives of O-notation</h3>
 <h3 id="conclusion">Conclusion</h3>
 <p>This concludes the first part of our complexity journey - complexities are, as we can see, a very powerful tool to identify what kind of algorithm we’re working with
 and to get a somewhat accurate answer about question one can have about programs, for example, runtime of a program.</p>
-<p>Next part will be about dynamic arrays and how we use them - especially how to implement a stack and queues.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat038/dat038" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Sorting </div> </a> <a href="/chalmers/dat038/dat038_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Dynamic Arrays </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>Next part will be about dynamic arrays and how we use them - especially how to implement a stack and queues.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat038/dat038" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Sorting </div> </a> <a href="/chalmers/dat038/dat038_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Dynamic Arrays </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -486,7 +486,7 @@ <h4 id="implementation-of-a-queue-using-a-dynamic-array">Implementation of a que
 <span class="line"><span style="color:var(--astro-code-foreground)">            self</span><span style="color:var(--astro-code-token-punctuation)">.</span><span style="color:var(--astro-code-foreground)">head </span><span style="color:var(--astro-code-token-keyword)">=</span><span style="color:var(--astro-code-token-constant)"> 0</span></span>
 <span class="line"><span style="color:var(--astro-code-foreground)">            self</span><span style="color:var(--astro-code-token-punctuation)">.</span><span style="color:var(--astro-code-foreground)">tail </span><span style="color:var(--astro-code-token-keyword)">=</span><span style="color:var(--astro-code-foreground)"> self</span><span style="color:var(--astro-code-token-punctuation)">.</span><span style="color:var(--astro-code-foreground)">tail </span><span style="color:var(--astro-code-token-keyword)">-</span><span style="color:var(--astro-code-foreground)"> self</span><span style="color:var(--astro-code-token-punctuation)">.</span><span style="color:var(--astro-code-foreground)">head </span><span style="color:var(--astro-code-token-keyword)">-</span><span style="color:var(--astro-code-token-constant)"> 1</span></span></code></pre>
 <p>That’s it for this part - in the next part we’ll cover something called ‘<strong>A</strong>bstract <strong>D</strong>ata <strong>T</strong>ypes’ or for short ADTs.
-We’ll define what a ADT is and what’s the difference between them and ordinary data structures.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat038/dat038_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Complexity (1) </div> </a> <a href="/chalmers/dat038/dat038_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Abstract Data Types </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+We’ll define what a ADT is and what’s the difference between them and ordinary data structures.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat038/dat038_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Complexity (1) </div> </a> <a href="/chalmers/dat038/dat038_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Abstract Data Types </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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index da71d910..dd40a376 100644
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@@ -560,7 +560,7 @@ <h3 id="summary">Summary</h3>
 <p>In my notes there is one way, I wrote it using slightly different syntax/language. But the takeaway is still the ADTs as in a concept -  all these ADTs build on the same basic idea/operations.</p>
 <p>I really liked the picture from the slides in my course so, I’ll put it here to visualize everything we have discussed today.
 <img src="/images/school/Summary.png" alt="Summary"></p>
-<p>In the next part we’ll begin with concept we mentioned today - Hash tables!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat038/dat038_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Dynamic Arrays </div> </a> <a href="/chalmers/dat038/dat038_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Hash Tables </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>In the next part we’ll begin with concept we mentioned today - Hash tables!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat038/dat038_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Dynamic Arrays </div> </a> <a href="/chalmers/dat038/dat038_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Hash Tables </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -611,7 +611,7 @@ <h3 id="alternatives-to-linear-probing">Alternatives to linear probing</h3>
 <h3 id="summary">Summary</h3>
 <p>There’s <strong>a lot</strong> to hashing and hash tables in general. But I think we’ll leave it here, one final thing I want to bring up is:</p>
 <p>Hash tables are not ordered! If we want to find a maximum value in a hash table - it will take linear time! Since there’s no underlying order.</p>
-<p>In the next part we’ll begin looking at trees - starting at <strong>B</strong>alanced <strong>S</strong>earch <strong>T</strong>rees or BSTs for short. We’ll actually compare them to Hash maps, since they are quite similar in some aspects.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat038/dat038_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Abstract Data Types </div> </a> <a href="/chalmers/dat038/dat038_6" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Trees </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>In the next part we’ll begin looking at trees - starting at <strong>B</strong>alanced <strong>S</strong>earch <strong>T</strong>rees or BSTs for short. We’ll actually compare them to Hash maps, since they are quite similar in some aspects.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat038/dat038_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Abstract Data Types </div> </a> <a href="/chalmers/dat038/dat038_6" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Trees </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -625,7 +625,7 @@ <h3 id="red-black-tree-summary">Red-black Tree Summary</h3>
 <p>Red-black trees are 2-3 trees implemented using a BST - they have the invariant that they have to correspond to a perfectly balanced 2-3 tree.</p>
 <p>Update strategy is: Insert in a way that break the rules on red nodes, then fix it.</p>
 <p>They have logarithmic performance - worst case the height is $2\ log(n)$</p>
-<p>This was the end of this part - it was a lot to process, it was a lot for me as well :). In the next part we’ll cover priority queues and how they can be implemented as a kind of tree :).</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat038/dat038_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Hash Tables </div> </a> <a href="/chalmers/dat038/dat038_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Binary Heaps </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>This was the end of this part - it was a lot to process, it was a lot for me as well :). In the next part we’ll cover priority queues and how they can be implemented as a kind of tree :).</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat038/dat038_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Hash Tables </div> </a> <a href="/chalmers/dat038/dat038_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Binary Heaps </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -351,7 +351,7 @@ <h3 id="summary--conclusion">Summary &#x26; Conclusion</h3>
 </ul>
 </li>
 </ul>
-<p>This was it for this quite short part - in the next part(s) we’ll begin the final part of this course - graphs!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat038/dat038_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Trees </div> </a> <a href="/chalmers/dat038/dat038_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Graphs </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>This was it for this quite short part - in the next part(s) we’ll begin the final part of this course - graphs!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat038/dat038_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Trees </div> </a> <a href="/chalmers/dat038/dat038_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Graphs </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -429,7 +429,7 @@ <h3 id="example-problems">Example Problems</h3>
 <p>There are many finding ‘connected components’ problems, here’s a good picture to illustrate what we can use and not:
 <img src="/images/school/Graphs.png" alt="Graphs"></p>
 <h3 id="conclusion">Conclusion</h3>
-<p>So that’s it for graphs - in the next part we’ll cover <em>minimum spanning trees</em> and <em>shortest path algorithms</em>.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat038/dat038_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Binary Heaps </div> </a> <a href="/chalmers/dat038/dat038_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Shortest Path &amp; Spanning Trees </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>So that’s it for graphs - in the next part we’ll cover <em>minimum spanning trees</em> and <em>shortest path algorithms</em>.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat038/dat038_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Binary Heaps </div> </a> <a href="/chalmers/dat038/dat038_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Shortest Path &amp; Spanning Trees </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -530,7 +530,7 @@ <h3 id="summary">Summary</h3>
 we can almost always use UCS/Dijkstras, since this is almost linear.</p>
 <p>If we encounter a DAG, we should perform a Topological sort algorithm, since it’s linear</p>
 <p>Negative weights and negative cycles, If we have no negative cycles - then Bellman-ford is the approach,
-otherwise we can find <strong>some path</strong> via Bellman-ford.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat038/dat038_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Graphs </div> </a> <a href="/chalmers/dat038/dat038_10" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Complexity (2) </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+otherwise we can find <strong>some path</strong> via Bellman-ford.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat038/dat038_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Graphs </div> </a> <a href="/chalmers/dat038/dat038_10" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Complexity (2) </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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-</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/chalmers/dat038/dat038_10" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 10 - Complexity (2) </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat038/dat038_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Shortest Path &amp; Spanning Trees </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat038/dat038_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Graphs </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat038/dat038_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Binary Heaps </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat038/dat038_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Trees </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat038/dat038_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Hash Tables </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat038/dat038_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Abstract Data Types </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat038/dat038_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Dynamic Arrays </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat038/dat038_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Complexity (1) </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat038/dat038" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Sorting </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/chalmers/dat038/dat038_10" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 10 - Complexity (2) </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat038/dat038_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Shortest Path &amp; Spanning Trees </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat038/dat038_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Graphs </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat038/dat038_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Binary Heaps </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat038/dat038_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Trees </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat038/dat038_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Hash Tables </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat038/dat038_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Abstract Data Types </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat038/dat038_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Dynamic Arrays </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat038/dat038_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Complexity (1) </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat038/dat038" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - 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@@ -303,7 +303,7 @@ <h3 id="properties-of-data">Properties of data</h3>
 <li>Even if the dataset is small, it can answer the right question given that the dataset is correct.</li>
 </ul>
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@@ -604,7 +604,7 @@ <h3 id="palmer-penguins">Palmer penguins</h3>
 <span class="line"><span style="color:var(--astro-code-foreground)">    plt</span><span style="color:var(--astro-code-token-punctuation)">.</span><span style="color:var(--astro-code-token-function)">legend</span><span style="color:var(--astro-code-token-punctuation)">()</span></span>
 <span class="line"></span>
 <span class="line"><span style="color:var(--astro-code-foreground)">plt</span><span style="color:var(--astro-code-token-punctuation)">.</span><span style="color:var(--astro-code-token-function)">show</span><span style="color:var(--astro-code-token-punctuation)">()</span></span></code></pre>
-<p><img src="/images/school/palmer.png#center" alt=""></p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat565/dat565" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Introduction </div> </a> <a href="/chalmers/dat565/dat565_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Data munging </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p><img src="/images/school/palmer.png#center" alt=""></p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat565/dat565" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Introduction </div> </a> <a href="/chalmers/dat565/dat565_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Data munging </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -314,7 +314,7 @@ <h3 id="regex-in-python">Regex in Python</h3>
 <li><code>re.search(regex, string)</code> returns a <code>Match</code> object to the first match of the regex in the string.</li>
 <li><code>re.findall(regex, string)</code> returns all non-overlapping matches of pattern in string (left-to-right).</li>
 <li><code>re.sub(regex, replacement, string)</code> replaces all occurrences of regex with replacement, the replacement can contain backreferences to groups in the match.</li>
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index c570e29b..83aebe4f 100644
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@@ -311,7 +311,7 @@ <h4 id="boxplot">Boxplot</h4>
 <p>The boxplot, or the box and whiskers plot, is a concise way to represent the different quartiles of the data.
 The box shows the upper and lower quartiles of the data
 (50% of the data lies inside the box, that is, the bottom of the box shows where 25% quartile is, and the top of the box where the 75% quartile is).</p>
-<p>The median of the data is shown with a line.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat565/dat565_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Data munging </div> </a> <a href="/chalmers/dat565/dat565_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Statistical analysis </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>The median of the data is shown with a line.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat565/dat565_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Data munging </div> </a> <a href="/chalmers/dat565/dat565_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Statistical analysis </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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diff --git a/chalmers/dat565/dat565_5/index.html b/chalmers/dat565/dat565_5/index.html
index 3df34873..cf007d1a 100644
--- a/chalmers/dat565/dat565_5/index.html
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@@ -509,7 +509,7 @@ <h3 id="logit-function">Logit function</h3>
 \lim_{x \to \infty} f(x) = 1 \newline
 \lim_{x \to -\infty} f(x) = 0 \newline
 \lim_{x \to 0} f(x) = \frac{1}{2}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat565/dat565_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Data visualization </div> </a> <a href="/chalmers/dat565/dat565_6" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Mathematical models </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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diff --git a/chalmers/dat565/dat565_6/index.html b/chalmers/dat565/dat565_6/index.html
index f258667b..3fb4ce0c 100644
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@@ -420,7 +420,7 @@ <h3 id="evaluating-regression-models">Evaluating regression models</h3>
 <p>A related statistic is the <strong>R</strong>oot <strong>M</strong>ean <strong>S</strong>quared that has the same units as the values themselves:
 $$
 RMS(\hat{y}, y) = \sqrt{MSE(\hat{y}, y)}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat565/dat565_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Statistical analysis </div> </a> <a href="/chalmers/dat565/dat565_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Linear and logistic regression </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat565/dat565_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Statistical analysis </div> </a> <a href="/chalmers/dat565/dat565_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Linear and logistic regression </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -325,7 +325,7 @@ <h3 id="maximum-likelihood-estimation">Maximum Likelihood Estimation</h3>
 This involves optimizing the log-likelihood function, which quantifies how well the model fits the data.</p>
 <h3 id="model-evaluation">Model Evaluation</h3>
 <p>Once the logistic regression model is trained, it is essential to evaluate its performance.
-Common metrics for evaluating classification models include accuracy, precision, recall, F1 score, and the receiver operating characteristic (ROC) curve.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat565/dat565_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Mathematical models </div> </a> <a href="/chalmers/dat565/dat565_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Distance and network methods </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+Common metrics for evaluating classification models include accuracy, precision, recall, F1 score, and the receiver operating characteristic (ROC) curve.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat565/dat565_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Mathematical models </div> </a> <a href="/chalmers/dat565/dat565_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Distance and network methods </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -306,7 +306,7 @@ <h3 id="rand-index">Rand index</h3>
 clusters in the predicted and true clusterings.</p>
 <p>$$
 RI = \frac{\text{Number of agreeing pairs}}{\text{Total number of pairs}}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat565/dat565_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Linear and logistic regression </div> </a> <a href="/chalmers/dat565/dat565_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Machine Learning </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat565/dat565_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Linear and logistic regression </div> </a> <a href="/chalmers/dat565/dat565_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Machine Learning </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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index bf6df9ea..ae08ab4e 100644
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@@ -549,7 +549,7 @@ <h4 id="pooling">Pooling</h4>
 <h4 id="fully-connected-layer">Fully connected layer</h4>
 <p>So, the power of CNNs is that they can learn local patterns in images. We can use CNNs to filter the important information from the image.
 From this new filtered image, if we flatten this new, smaller image, we can feed this into our network just like before.</p>
-<p>This is called a fully connected layer. It is the same as the hidden layer in a regular neural network.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat565/dat565_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Distance and network methods </div> </a> <div class="invisible"></div> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>This is called a fully connected layer. It is the same as the hidden layer in a regular neural network.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/dat565/dat565_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Distance and network methods </div> </a> <div class="invisible"></div> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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diff --git a/chalmers/dat565/index.html b/chalmers/dat565/index.html
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 </button> </nav> </div> </div> </header> <main>  <div class="mx-auto max-w-screen-sm px-3"> <h1 class="mb-6 text-3xl font-bold"> Introduction To Data Science And Ai (DAT565)
-</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/chalmers/dat565/dat565_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Machine Learning </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat565/dat565_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Distance and network methods </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat565/dat565_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Linear and logistic regression </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat565/dat565_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Mathematical models </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat565/dat565_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Statistical analysis </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat565/dat565_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Data visualization </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat565/dat565_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Data munging </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat565/dat565_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Python tools for data science </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat565/dat565" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Introduction </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/chalmers/dat565/dat565_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Machine Learning </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat565/dat565_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Distance and network methods </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat565/dat565_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Linear and logistic regression </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat565/dat565_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Mathematical models </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat565/dat565_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - 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Data munging </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat565/dat565_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Python tools for data science </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/dat565/dat565" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - 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@@ -343,7 +343,7 @@ <h1 id="logical-minimization">Logical Minimization</h1>
 <li><strong>Implicant</strong>, a product of variables of a function, f, for which f gets the value ‘1’.</li>
 <li><strong>Prime Implicant</strong>, an <em>implicant</em> that cannot be covered by a more general implicant.</li>
 <li><strong>Essential Prime Implicant</strong>, a prime implicant of a function, f, that includes a minterm, not included by any other prime implicant of the function.</li>
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@@ -293,7 +293,7 @@ <h3 id="carry-look-ahead-adders">Carry Look-ahead Adders</h3>
 r_i = p_i\ \oplus\ c_i
 $$</p>
 <h3 id="summary">Summary</h3>
-<p>This was quite a short part, but adders are quite a simple, yet powerful concept.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda322/eda322" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Introduction &amp; Boolean Algebra </div> </a> <a href="/chalmers/eda322/eda322_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Sequential Circuits </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>This was quite a short part, but adders are quite a simple, yet powerful concept.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda322/eda322" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Introduction &amp; Boolean Algebra </div> </a> <a href="/chalmers/eda322/eda322_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Sequential Circuits </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -320,7 +320,7 @@ <h3 id="examples">Examples</h3>
 <li>Choose flip-flops</li>
 <li>Derive logic expressions for state and outputs</li>
 <li>Implementation</li>
-</ul> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda322/eda322_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Binary Adders </div> </a> <a href="/chalmers/eda322/eda322_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Finite State Machines </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+</ul> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda322/eda322_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Binary Adders </div> </a> <a href="/chalmers/eda322/eda322_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Finite State Machines </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -299,7 +299,7 @@ <h4 id="partition">Partition</h4>
 $$
 P_2 = (ABD)(CEFG)
 $$</p>
-<p>Here, $(ABD)$ and $(CEFG)$ are “blocks”.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda322/eda322_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Sequential Circuits </div> </a> <a href="/chalmers/eda322/eda322_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Arithmetic Units </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>Here, $(ABD)$ and $(CEFG)$ are “blocks”.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda322/eda322_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Sequential Circuits </div> </a> <a href="/chalmers/eda322/eda322_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Arithmetic Units </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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index f0e5ffb4..8104682d 100644
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@@ -336,7 +336,7 @@ <h3 id="fixed-point--floating-point-numbers">Fixed-point &#x26; Floating-point n
 <p>Which represents:
 $$
 v = \frac{18}{32} \cdot\ 8
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda322/eda322_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Finite State Machines </div> </a> <a href="/chalmers/eda322/eda322_6" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Reconfigurable Hardware </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda322/eda322_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Finite State Machines </div> </a> <a href="/chalmers/eda322/eda322_6" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Reconfigurable Hardware </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -378,7 +378,7 @@ <h3 id="summary">Summary</h3>
 second supports only a predefined –during fabrication- finite number of
 functions.
 – Stamatis Vassiliadis</p>
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@@ -350,7 +350,7 @@ <h3 id="metrics">Metrics</h3>
 $$
 P_{peak} = \max\left(\lim_{\Delta t \rightarrow 0}\ \frac{\Delta E}{\Delta T}\right) = \max\left(\frac{dE}{dt}\right)
 $$</p>
-<p>One of the most popular metrics is <strong>performance per watt</strong> (measures energy efficiency).</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda322/eda322_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Reconfigurable Hardware </div> </a> <a href="/chalmers/eda322/eda322_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Interfaces and Memory </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>One of the most popular metrics is <strong>performance per watt</strong> (measures energy efficiency).</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda322/eda322_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Reconfigurable Hardware </div> </a> <a href="/chalmers/eda322/eda322_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Interfaces and Memory </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -381,7 +381,7 @@ <h3 id="memory">Memory</h3>
 <li>1Mbit x 8 EPROM can implement 8 independent functions each of $log_2(1M) = 20$ inputs.</li>
 <li>The decoder part of a memory block can be considered a “minterm generator”.</li>
 <li>The cell array part of a memory block can be considered an OR function over a subset of rows.</li>
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@@ -378,7 +378,7 @@ <h3 id="algorithm-for-path-sensitization">Algorithm for “path sensitization”
 </ul>
 </li>
 <li>If a conflict arises, we look for another way for justification.</li>
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index 9f24719c..eb563f14 100644
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-</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/chalmers/eda322/eda322_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Testing </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda322/eda322_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Interfaces and Memory </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda322/eda322_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Timing, delay &amp; power </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda322/eda322_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Reconfigurable Hardware </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda322/eda322_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Arithmetic Units </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda322/eda322_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Finite State Machines </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda322/eda322_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Sequential Circuits </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda322/eda322_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Binary Adders </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda322/eda322" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Introduction &amp; Boolean Algebra </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/chalmers/eda322/eda322_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Testing </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda322/eda322_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Interfaces and Memory </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda322/eda322_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Timing, delay &amp; power </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda322/eda322_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Reconfigurable Hardware </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda322/eda322_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Arithmetic Units </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda322/eda322_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Finite State Machines </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda322/eda322_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Sequential Circuits </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda322/eda322_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Binary Adders </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda322/eda322" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Introduction &amp; Boolean Algebra </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -363,7 +363,7 @@ <h4 id="conditional-jumps">Conditional jumps</h4>
 <p>Notice how there isn’t any usual <code>blt, bge</code>, since MIPS is of RISC architecture, we don’t need those.</p>
 <p>Instead, what we can do is using <code>slt</code>. Which stands for set less than, we can now use this to replicate a <code>blt</code> or <code>bge</code>.</p>
 <p>However, <code>blt, bge</code> are still pseudo-keywords in MIPS. The assembler will still be able to interpret these.</p>
-<p>On the topic of pseudo-keywords, things like <code>move</code> and <code>li</code> are also pseudo-keywords.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/chalmers/eda333/eda333_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - MIPS </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>On the topic of pseudo-keywords, things like <code>move</code> and <code>li</code> are also pseudo-keywords.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/chalmers/eda333/eda333_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - MIPS </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -371,7 +371,7 @@ <h3 id="common-mistakes">Common mistakes</h3>
 <li>
 <p>MIPS uses byte addressing</p>
 </li>
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@@ -493,7 +493,7 @@ <h3 id="summary">Summary</h3>
 </ul>
 <p>That last one might not be so clear from the start, but if we had very complex functions like</p>
 <pre class="astro-code css-variables" style="background-color:var(--astro-code-background);color:var(--astro-code-foreground); overflow-x: auto;" tabindex="0" data-language="plaintext"><code><span class="line"><span>add M[$t0], M[$t1], M[$t2]</span></span></code></pre>
-<p>This would be a headache, since then we are in the execute stage and read/write to memory simultaneously.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda333/eda333_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - MIPS </div> </a> <a href="/chalmers/eda333/eda333_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Pipeline hardware </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>This would be a headache, since then we are in the execute stage and read/write to memory simultaneously.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda333/eda333_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - MIPS </div> </a> <a href="/chalmers/eda333/eda333_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Pipeline hardware </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -536,7 +536,7 @@ <h3 id="summary">Summary</h3>
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-</ul> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda333/eda333_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Pipelining </div> </a> <a href="/chalmers/eda333/eda333_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Cache memory </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+</ul> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda333/eda333_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Pipelining </div> </a> <a href="/chalmers/eda333/eda333_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Cache memory </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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index 536ae243..7d7c3739 100644
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@@ -406,7 +406,7 @@ <h3 id="multiple-level-cache">Multiple-level cache</h3>
 <h3 id="floating-point">Floating-point</h3>
 <p>$$
 x = (-1)^S \cdot\ (1 + Fraction) \cdot\ 2^{Exponent - Bias}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda333/eda333_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Pipeline hardware </div> </a> <a href="/chalmers/eda333/eda333_6" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Virtual Memory </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -494,7 +494,7 @@ <h3 id="memory-summary">Memory summary</h3>
 <p>Small memories are fast - bigger memories come with the cost of longer access times.</p>
 <p>Caches give us this illusion of big memory with short access times.
 Much due to the principle of locality.</p>
-<p>Remember that our hierarchy of memory is from smallest with the shortest access time to biggest with the longest access time!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda333/eda333_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Cache memory </div> </a> <a href="/chalmers/eda333/eda333_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Floating-point arithmetic </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>Remember that our hierarchy of memory is from smallest with the shortest access time to biggest with the longest access time!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda333/eda333_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Cache memory </div> </a> <a href="/chalmers/eda333/eda333_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Floating-point arithmetic </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -310,7 +310,7 @@ <h3 id="floating-point-in-mips">Floating-point in MIPS</h3>
 <span class="line"><span>c.condition.s, c.condition.d</span></span>
 <span class="line"><span></span></span>
 <span class="line"><span>bc1t, bc1f</span></span></code></pre>
-<p>It sets a special floating-point condition bit, therefore, the branches take no operands.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda333/eda333_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Virtual Memory </div> </a> <a href="/chalmers/eda333/eda333_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Parallel Processors </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -295,7 +295,7 @@ <h3 id="cache-coherence">Cache Coherence</h3>
 <p>Just as in concurrent programming, we have two paradigms, shared memory and message passing.</p>
 <p>For our <strong>S</strong>hare <strong>M</strong>emory multi<strong>P</strong>rocessor, we need to use synchronization primitives, to avoid cache invalidation.</p>
 <p>We can solve these problems using FSMs as well to set up a clear protocol.</p>
-<p>For message passing, we do not share memory - but we send messages between processors to synchronize.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda333/eda333_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Floating-point arithmetic </div> </a> <a href="/chalmers/eda333/eda333_summary" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Summary </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>For message passing, we do not share memory - but we send messages between processors to synchronize.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda333/eda333_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Floating-point arithmetic </div> </a> <a href="/chalmers/eda333/eda333_summary" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Summary </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -388,7 +388,7 @@ <h3 id="notes">Notes</h3>
 <p>TLB Index: If there are E pages, index = log2(E).</p>
 <p>TLB Tag: Tag is the rest of bits. So, if we have V virtual address bits, tag = V - index.</p>
 <p>Calculate the size of each <strong>block entry</strong>. = Number of status bits (valid, dirt etc). + Tag bits + Data bits (Usually block size (in bytes) * 8).</p>
-<p>Calculate the size of the cache. = Number of status bits (valid, dirt etc). + Tag bits + Data bits (Usually block size (in bytes) * 8).</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda333/eda333_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Parallel Processors </div> </a> <div class="invisible"></div> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>Calculate the size of the cache. = Number of status bits (valid, dirt etc). + Tag bits + Data bits (Usually block size (in bytes) * 8).</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eda333/eda333_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Parallel Processors </div> </a> <div class="invisible"></div> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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-</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/chalmers/eda333/eda333_summary" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Summary </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda333/eda333_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Parallel Processors </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda333/eda333_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Floating-point arithmetic </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda333/eda333_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Virtual Memory </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda333/eda333_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Cache memory </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda333/eda333_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Pipeline hardware </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda333/eda333_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Pipelining </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda333/eda333_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - MIPS </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda333/eda333" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Introduction </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/chalmers/eda333/eda333_summary" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Summary </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda333/eda333_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Parallel Processors </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda333/eda333_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Floating-point arithmetic </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda333/eda333_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Virtual Memory </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda333/eda333_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Cache memory </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda333/eda333_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Pipeline hardware </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda333/eda333_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Pipelining </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda333/eda333_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - MIPS </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eda333/eda333" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - 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@@ -315,7 +315,7 @@ <h4 id="kirchhoffs-voltage-law">Kirchhoff’s voltage law</h4>
 $$</p>
 <p>Since we earlier defined what is considered positive and negative voltage, we understand if we go from - to +, we need to subtract that voltage, and the other way around for + to -.</p>
 <h3 id="summary">Summary</h3>
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+<p>This concludes this first part - in short - we’ll use these concepts and formulas for all problems we encounter in the future, so it’s important to precisely define and deeply understand them.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/chalmers/eem076/eem076_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Power &amp; Energy </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -422,7 +422,7 @@ <h3 id="impedance">Impedance</h3>
 I(t) = 16 cos(3000t - 126.9^\circ) mA
 $$</p>
 <p>Just as we predicted, the current lags behind by a lot!</p>
-<p>As we can see, our new tools and knowledge about how we can use complex numbers are quite powerful!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076_9" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Electromagnetic Waves </div> </a> <a href="/chalmers/eem076/eem076_11" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 11 - Calculation methods for AC-circuits </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>As we can see, our new tools and knowledge about how we can use complex numbers are quite powerful!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076_9" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Electromagnetic Waves </div> </a> <a href="/chalmers/eem076/eem076_11" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 11 - Calculation methods for AC-circuits </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -573,7 +573,7 @@ <h3 id="resonance">Resonance</h3>
 B &#x26; = f_H - f_L \newline
 &#x26; = \dfrac{f_0}{Q_s}
 \end{align*}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076_10" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Steady-state sinusoidal analysis </div> </a> <a href="/chalmers/eem076/eem076_12" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 12 - Power in AC Circuits </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076_10" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Steady-state sinusoidal analysis </div> </a> <a href="/chalmers/eem076/eem076_12" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 12 - Power in AC Circuits </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -415,7 +415,7 @@ <h3 id="power-relationships">Power Relationships</h3>
 $$</p>
 <p>$$
 S = \dfrac{V_m I_m}{2} \angle \theta_V - \phi_I
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076_11" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 11 - Calculation methods for AC-circuits </div> </a> <a href="/chalmers/eem076/eem076_13" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 13 - Op-Amps and Filters </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -338,7 +338,7 @@ <h3 id="operational-amplifier-op-amp">Operational Amplifier (Op-Amp)</h3>
 <li>Verify that negative feedback is present</li>
 <li>Assume that the voltage between the terminals and input current are forced to 0.</li>
 <li>Apply standard circuit analysis principles (KCL, KVL, and Ohm’s Law).</li>
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@@ -334,7 +334,7 @@ <h3 id="current-and-voltage-dividers">Current and Voltage dividers</h3>
 $$
 I_1 = \frac{V}{R_1} = I_{total}\ \frac{R_2}{(R_1 + R_2)} \newline
 I_2 = \frac{V}{R_2} = I_{total}\ \frac{R_1}{(R_1 + R_2)} \newline
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Introduction </div> </a> <a href="/chalmers/eem076/eem076_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Equivalent circuits </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -424,7 +424,7 @@ <h3 id="source-transformation">Source transformation</h3>
 V_{TH} = I_{N} \cdot\ R_{eq}
 $$</p>
 <p>Using Ohm’s law, we can easily just convert one type of circuit to the corresponding other type!</p>
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+<p>We’ll be using this tool a lot in future for analyzing circuits!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Power &amp; Energy </div> </a> <a href="/chalmers/eem076/eem076_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Capacitance and Inductance </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -411,7 +411,7 @@ <h3 id="time-varying-circuits">Time-Varying Circuits</h3>
 $$
 I(t) = I_{0}\ e^{\frac{-Rt}{L}} \newline
 \tau = \frac{L}{R}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Equivalent circuits </div> </a> <a href="/chalmers/eem076/eem076_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Electrical fields </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Equivalent circuits </div> </a> <a href="/chalmers/eem076/eem076_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Electrical fields </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -351,7 +351,7 @@ <h3 id="gausss-law">Gauss’s law</h3>
 <h4 id="gaussian-surfaces">Gaussian surfaces</h4>
 <p>Since this is from a specific surface, we’ll need to consider the different types:
 <img src="/images/school/GS.png#center" alt=""></p>
-<p>These are the gaussian surfaces that we’ll be looking into!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Capacitance and Inductance </div> </a> <a href="/chalmers/eem076/eem076_6" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Work, Voltage and Capacitance </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>These are the gaussian surfaces that we’ll be looking into!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Capacitance and Inductance </div> </a> <a href="/chalmers/eem076/eem076_6" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Work, Voltage and Capacitance </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -389,7 +389,7 @@ <h3 id="energy-stored-in-capacitors">Energy stored in capacitors</h3>
 <p>Where, $u$, is called the electrical field density:
 $$
 u = \dfrac{\varepsilon_0 E^2}{2}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Electrical fields </div> </a> <a href="/chalmers/eem076/eem076_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Electrical &amp; Magnetic fields </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Electrical fields </div> </a> <a href="/chalmers/eem076/eem076_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Electrical &amp; Magnetic fields </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -351,7 +351,7 @@ <h3 id="amperes-law">Ampere’s law</h3>
 $$
 \oint \mathbf{\vec{B}} \cdot\ d\mathbf{\vec{s}} = \mu_0 I_{enc}
 $$</p>
-<p>Note that this equation requires symmetry (in this case infinite symmetry!).</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Work, Voltage and Capacitance </div> </a> <a href="/chalmers/eem076/eem076_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Magnetic fields </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>Note that this equation requires symmetry (in this case infinite symmetry!).</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Work, Voltage and Capacitance </div> </a> <a href="/chalmers/eem076/eem076_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Magnetic fields </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -368,7 +368,7 @@ <h3 id="generators-and-motors">Generators and motors</h3>
 $$
 P = I |\varepsilon| = \dfrac{(NBA \omega)^2}{R} sin^2 (\omega t)
 $$</p>
-<p>We can see that, it’s just the absolute value of the alternating current!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Electrical &amp; Magnetic fields </div> </a> <a href="/chalmers/eem076/eem076_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Electromagnetic Waves </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>We can see that, it’s just the absolute value of the alternating current!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Electrical &amp; Magnetic fields </div> </a> <a href="/chalmers/eem076/eem076_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Electromagnetic Waves </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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index cb35e359..f70fb8ba 100644
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@@ -419,7 +419,7 @@ <h3 id="emfs-in-circuits">EMFs in circuits</h3>
 V(t) = L \dfrac{dI}{dt}
 $$</p>
 </blockquote>
-<p>We can now use this knowledge to understand LC and RLC circuits - and see how and why the energy oscillates between the electrical and magnetic field!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Magnetic fields </div> </a> <a href="/chalmers/eem076/eem076_10" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Steady-state sinusoidal analysis </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 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+<p>We can now use this knowledge to understand LC and RLC circuits - and see how and why the energy oscillates between the electrical and magnetic field!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/eem076/eem076_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Magnetic fields </div> </a> <a href="/chalmers/eem076/eem076_10" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Steady-state sinusoidal analysis </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 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@@ -809,7 +809,7 @@ <h3 id="ac">AC</h3>
 <li>
 <p>Apparent Power: $|S| = V_{rms} I_{rms} [VA]$.</p>
 </li>
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-</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/chalmers/eem076/eem076_summary" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 14 - Summary </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_13" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 13 - Op-Amps and Filters </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_12" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 12 - Power in AC Circuits </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_11" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 11 - Calculation methods for AC-circuits </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_10" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 10 - Steady-state sinusoidal analysis </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Electromagnetic Waves </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Magnetic fields </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Electrical &amp; Magnetic fields </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Work, Voltage and Capacitance </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Electrical fields </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Capacitance and Inductance </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Equivalent circuits </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Power &amp; Energy </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Introduction </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/chalmers/eem076/eem076_summary" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 14 - Summary </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_13" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 13 - Op-Amps and Filters </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_12" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 12 - Power in AC Circuits </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_11" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 11 - Calculation methods for AC-circuits </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_10" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 10 - Steady-state sinusoidal analysis </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Electromagnetic Waves </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Magnetic fields </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Electrical &amp; Magnetic fields </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Work, Voltage and Capacitance </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Electrical fields </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Capacitance and Inductance </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Equivalent circuits </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Power &amp; Energy </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/eem076/eem076" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Introduction </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -336,7 +336,7 @@ <h4 id="feedback-systems">Feedback systems</h4>
 <p>Here, the control signal, $u(t)$, is determined by measuring the actual output, $y(t)$.
 It has the advantage of adjusting its behavior based on feedback, ensuring the system stays on track.
 Control error, $e(t)$, represents the difference between the desired and actual output.
-Minimizing this error is a primary objective in control theory.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/chalmers/ere103/ere103_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Transfer functions </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+Minimizing this error is a primary objective in control theory.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/chalmers/ere103/ere103_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Transfer functions </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -413,7 +413,7 @@ <h3 id="example-1">Example</h3>
 $$</p>
 <p>$$
 K_p = \ldots \approx 166.31
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_9" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - General controller structure </div> </a> <a href="/chalmers/ere103/ere103_11" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 11 - Design of controllers (2) </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_9" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - General controller structure </div> </a> <a href="/chalmers/ere103/ere103_11" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 11 - Design of controllers (2) </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -337,7 +337,7 @@ <h3 id="ziegler-nichols-method">Ziegler-Nichols method</h3>
 
 
 
-<table><thead><tr><th align="center"></th><th align="center"></th><th align="center"></th><th align="center"></th></tr></thead><tbody><tr><td align="center"></td><td align="center">$K_p$</td><td align="center">$T_i$</td><td align="center">$T_d$</td></tr><tr><td align="center">P-controller</td><td align="center">$0.5K_0$</td><td align="center">-</td><td align="center">-</td></tr><tr><td align="center">PI-controller</td><td align="center">$0.45K_0$</td><td align="center">$0.85T_0$</td><td align="center">-</td></tr><tr><td align="center">PID-controller</td><td align="center">$0.6K_0$</td><td align="center">$0.5T_0$</td><td align="center">$0.125 T_0$</td></tr></tbody></table> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_10" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Design of controllers </div> </a> <a href="/chalmers/ere103/ere103_12" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 12 - State feedback </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 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+<table><thead><tr><th align="center"></th><th align="center"></th><th align="center"></th><th align="center"></th></tr></thead><tbody><tr><td align="center"></td><td align="center">$K_p$</td><td align="center">$T_i$</td><td align="center">$T_d$</td></tr><tr><td align="center">P-controller</td><td align="center">$0.5K_0$</td><td align="center">-</td><td align="center">-</td></tr><tr><td align="center">PI-controller</td><td align="center">$0.45K_0$</td><td align="center">$0.85T_0$</td><td align="center">-</td></tr><tr><td align="center">PID-controller</td><td align="center">$0.6K_0$</td><td align="center">$0.5T_0$</td><td align="center">$0.125 T_0$</td></tr></tbody></table> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_10" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Design of controllers </div> </a> <a href="/chalmers/ere103/ere103_12" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 12 - State feedback </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 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@@ -569,7 +569,7 @@ <h3 id="example">Example</h3>
 <p>This is just some basic matrix operations:
 $$
 K_r = \ldots = \boxed{4}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_11" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 11 - Design of controllers (2) </div> </a> <a href="/chalmers/ere103/ere103_13" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 13 - Discretization </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_11" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 11 - Design of controllers (2) </div> </a> <a href="/chalmers/ere103/ere103_13" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 13 - Discretization </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -282,7 +282,7 @@ <h3 id="delay-theorem">Delay Theorem</h3>
 <h3 id="controller-design-based-on-analog-gs-and-fs">Controller design based on analog $G(s)$ and $F(s)$</h3>
 <p>The discretization of $L_d(z) = F_d(z) G_d(z)$</p>
 <p>Sensitivity function, $S_d(z) = \dfrac{1}{1 + L_d(z)}$
-Inverse sensitivity function, $S_d(z) = \dfrac{L_d(z)}{1 + L_d(z)}$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_12" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 12 - State feedback </div> </a> <a href="/chalmers/ere103/ere103_14" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 14 - Filters </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+Inverse sensitivity function, $S_d(z) = \dfrac{L_d(z)}{1 + L_d(z)}$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_12" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 12 - State feedback </div> </a> <a href="/chalmers/ere103/ere103_14" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 14 - Filters </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -286,7 +286,7 @@ <h3 id="filter-transformation">Filter transformation</h3>
 <p>In the case we had a second order filter:
 $$
 G(s) = \dfrac{1}{\frac{s^2}{\omega_c^2} + \sqrt{2} \frac{s}{\omega_c} + 1} = \dfrac{\omega_c^2}{s^2 + \sqrt{2}\omega_c s + \omega_c^2}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_13" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 13 - Discretization </div> </a> <a href="/chalmers/ere103/ere103_summary" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 15 - Summary </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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index 4a29379a..f1d73469 100644
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@@ -368,7 +368,7 @@ <h3 id="unit-step-function">Unit step function</h3>
 <p>Using partial fraction decomposition:
 $$
 G(s) = \dfrac{K}{s} - \dfrac{KT}{1 + sT}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Introduction </div> </a> <a href="/chalmers/ere103/ere103_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Controllers in the Laplace domain </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Introduction </div> </a> <a href="/chalmers/ere103/ere103_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Controllers in the Laplace domain </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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index a5ef66db..a7deb266 100644
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@@ -473,7 +473,7 @@ <h3 id="example-pi-controller">Example PI-controller</h3>
 <p>$$
 \boxed{\lim_{t \to \infty} y(t) = r_0}
 $$</p>
-<p>So, we see that a PI-controller gets us exactly the reference value.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Transfer functions </div> </a> <a href="/chalmers/ere103/ere103_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Models for mechanical systems </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>So, we see that a PI-controller gets us exactly the reference value.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Transfer functions </div> </a> <a href="/chalmers/ere103/ere103_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Models for mechanical systems </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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index 2ce61ab8..e3ce1263 100644
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@@ -293,7 +293,7 @@ <h3 id="example-tank-system">Example tank system</h3>
 <p>$$
 \dot{h} = \dfrac{1}{A}(q_{in} - a \sqrt{2g} \cdot \sqrt{h_1})
 $$</p>
-<p>In the next part, we’ll see how we can linearize this function to obtain the so-called space-state representation of this system.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Controllers in the Laplace domain </div> </a> <a href="/chalmers/ere103/ere103_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Space-state representation (1) </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>In the next part, we’ll see how we can linearize this function to obtain the so-called space-state representation of this system.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Controllers in the Laplace domain </div> </a> <a href="/chalmers/ere103/ere103_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Space-state representation (1) </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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diff --git a/chalmers/ere103/ere103_5/index.html b/chalmers/ere103/ere103_5/index.html
index 79bfef07..955d999e 100644
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@@ -343,7 +343,7 @@ <h3 id="example-tank-system">Example tank system</h3>
 <p>Let $K = \dfrac{2h_0}{q_0}$ and $T = \dfrac{2Ah_0}{q_0}$
 $$
 G_{qh}(s) = \dfrac{K}{1 + sT} \ | \div q_0
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Models for mechanical systems </div> </a> <a href="/chalmers/ere103/ere103_6" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Space-state representation (2) </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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index bee21a06..901682c3 100644
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@@ -389,7 +389,7 @@ <h3 id="from-transfer-function-to-space-state-representation">From transfer func
 u \newline
 y = x_1
 \end{cases}}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Space-state representation (1) </div> </a> <a href="/chalmers/ere103/ere103_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Bode plot </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Space-state representation (1) </div> </a> <a href="/chalmers/ere103/ere103_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Bode plot </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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index e989e487..cbacecf1 100644
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@@ -503,7 +503,7 @@ <h4 id="example-4">Example</h4>
 <p>This is now in standard form.
 $$
 G(j\omega) = \boxed{\dfrac{0.5(1 + j\omega)e^{-0.5j\omega}}{j\omega(1 + \frac{j\omega}{2})(1 + \frac{j\omega}{3})}}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Space-state representation (2) </div> </a> <a href="/chalmers/ere103/ere103_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Stability </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Space-state representation (2) </div> </a> <a href="/chalmers/ere103/ere103_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Stability </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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diff --git a/chalmers/ere103/ere103_8/index.html b/chalmers/ere103/ere103_8/index.html
index 616c6c40..6c26fb48 100644
--- a/chalmers/ere103/ere103_8/index.html
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@@ -580,7 +580,7 @@ <h3 id="nyquist-criterion">Nyquist criterion</h3>
 $$
 Z = N + P = 0
 $$</p>
-<p>Then the system is said to be stable.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Bode plot </div> </a> <a href="/chalmers/ere103/ere103_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - General controller structure </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>Then the system is said to be stable.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Bode plot </div> </a> <a href="/chalmers/ere103/ere103_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - General controller structure </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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diff --git a/chalmers/ere103/ere103_9/index.html b/chalmers/ere103/ere103_9/index.html
index 1c5d3bea..44459db9 100644
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@@ -312,7 +312,7 @@ <h3 id="example">Example</h3>
 $$</p>
 <p>$$
 \zeta = \dfrac{1}{2 \omega_n} = \dfrac{1}{2 \sqrt{0.1K_p}}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Stability </div> </a> <a href="/chalmers/ere103/ere103_10" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Design of controllers </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Stability </div> </a> <a href="/chalmers/ere103/ere103_10" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Design of controllers </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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diff --git a/chalmers/ere103/ere103_summary/index.html b/chalmers/ere103/ere103_summary/index.html
index d1248da6..5010d981 100644
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@@ -484,7 +484,7 @@ <h3 id="nyquists-criterion">Nyquists criterion</h3>
 $$</p>
 <p>$$
 N = \text{Number of turns } L(j\omega) \text{ has around } (-1, 0) \text{ clockwise.}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ere103/ere103_14" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 14 - Filters </div> </a> <div class="invisible"></div> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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 </button> </nav> </div> </div> </header> <main>  <div class="mx-auto max-w-screen-sm px-3"> <h1 class="mb-6 text-3xl font-bold"> Control Theory (ERE103)
-</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/chalmers/ere103/ere103_summary" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 15 - Summary </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_14" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 14 - Filters </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_13" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 13 - Discretization </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_12" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 12 - State feedback </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_11" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 11 - Design of controllers (2) </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_10" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 10 - Design of controllers </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - General controller structure </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Stability </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Bode plot </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Space-state representation (2) </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Space-state representation (1) </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Models for mechanical systems </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Controllers in the Laplace domain </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Transfer functions </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Introduction </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/chalmers/ere103/ere103_summary" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 15 - Summary </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_14" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 14 - Filters </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_13" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 13 - Discretization </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_12" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 12 - State feedback </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_11" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 11 - Design of controllers (2) </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_10" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 10 - Design of controllers </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - General controller structure </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Stability </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Bode plot </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Space-state representation (2) </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Space-state representation (1) </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Models for mechanical systems </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Controllers in the Laplace domain </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Transfer functions </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ere103/ere103" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - 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-</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/chalmers/lma017/lma017_summary" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 21 - Summary </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_20" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 20 - Divergence and Stokes&#39; Theorem </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_19" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 19 - Surface integrals </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_18" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 18 - Green&#39;s Theorem </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_17" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 17 - Gradient theorem </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_16" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 16 - Vector fields </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_15" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 15 - Line integrals </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_14" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 14 - Curves </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_13" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 13 - The Jacobian </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_12" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 12 - Change of variables </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_11" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 11 - General regions (2) </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_10" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 10 - General regions (1) </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Double and triple integrals </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Lagrange multipliers </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Absolute max and min values </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Maximum and minimum values </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Directional derivatives </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Chain rule </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Higher partial derivatives </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Continuity &amp; partial derivatives. </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Functions of several variables </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/chalmers/lma017/lma017_summary" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 21 - Summary </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_20" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 20 - Divergence and Stokes&#39; Theorem </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_19" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 19 - Surface integrals </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_18" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 18 - Green&#39;s Theorem </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_17" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 17 - Gradient theorem </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_16" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 16 - Vector fields </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_15" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 15 - Line integrals </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_14" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 14 - Curves </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_13" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 13 - The Jacobian </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_12" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 12 - Change of variables </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_11" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 11 - General regions (2) </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_10" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 10 - General regions (1) </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Double and triple integrals </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Lagrange multipliers </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Absolute max and min values </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Maximum and minimum values </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Directional derivatives </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Chain rule </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Higher partial derivatives </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Continuity &amp; partial derivatives. </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/lma017/lma017" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Functions of several variables </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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10.5C5.067 10.5 3.5 8.933 3.5 7ZM9.96544 11.0261C9.13578 11.6382 8.11014 12 7 12C4.23858 12 2 9.76142 2 7C2 4.23858 4.23858 2 7 2C9.76142 2 12 4.23858 12 7C12 8.11014 11.6382 9.13578 11.0261 9.96544L14.0303 12.9697L14.5607 13.5L13.5 14.5607L12.9697 14.0303L9.96544 11.0261Z" fill="currentColor"></path> </svg>
@@ -324,7 +324,7 @@ <h3 id="limits">Limits</h3>
 </ol>
 <p>$$
 \lim_{(x, y) \to (a, b)} \dfrac{f(x, y)}{h(x, y} = \dfrac{L}{M} , M \neq 0
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/chalmers/lma017/lma017_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Continuity &amp; partial derivatives. </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/chalmers/lma017/lma017_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Continuity &amp; partial derivatives. </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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diff --git a/chalmers/lma017/lma017_10/index.html b/chalmers/lma017/lma017_10/index.html
index 0ed76d46..51bcc932 100644
--- a/chalmers/lma017/lma017_10/index.html
+++ b/chalmers/lma017/lma017_10/index.html
@@ -1,4 +1,4 @@
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10.5C5.067 10.5 3.5 8.933 3.5 7ZM9.96544 11.0261C9.13578 11.6382 8.11014 12 7 12C4.23858 12 2 9.76142 2 7C2 4.23858 4.23858 2 7 2C9.76142 2 12 4.23858 12 7C12 8.11014 11.6382 9.13578 11.0261 9.96544L14.0303 12.9697L14.5607 13.5L13.5 14.5607L12.9697 14.0303L9.96544 11.0261Z" fill="currentColor"></path> </svg>
@@ -409,7 +409,7 @@ <h3 id="example-2">Example</h3>
 $$</p>
 <p>$$
 \boxed{\dfrac{1}{2} \left(-cos(1) + 1 \right)}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_9" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Double and triple integrals </div> </a> <a href="/chalmers/lma017/lma017_11" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 11 - General regions (2) </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_9" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Double and triple integrals </div> </a> <a href="/chalmers/lma017/lma017_11" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 11 - General regions (2) </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -408,7 +408,7 @@ <h3 id="properties-of-triple-integrals">Properties of triple integrals</h3>
 <p>However:
 5) $\iint_D 1\ dA$ = Area over D.</p>
 <p>In the triple integral case:
-5) $\iiint_E 1\ dV$ = Volume over solid.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_10" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - General regions (1) </div> </a> <a href="/chalmers/lma017/lma017_12" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 12 - Change of variables </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+5) $\iiint_E 1\ dV$ = Volume over solid.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_10" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - General regions (1) </div> </a> <a href="/chalmers/lma017/lma017_12" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 12 - Change of variables </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -315,7 +315,7 @@ <h3 id="example-1">Example</h3>
 $$</p>
 <p>$$
 \int_0^{\pi} \int_1^2 r^{17} cos^2(\theta)\ dr\ d\theta = \ldots = \boxed{\pi}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_11" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 11 - General regions (2) </div> </a> <a href="/chalmers/lma017/lma017_13" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 13 - The Jacobian </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_11" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 11 - General regions (2) </div> </a> <a href="/chalmers/lma017/lma017_13" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 13 - The Jacobian </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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--- a/chalmers/lma017/lma017_13/index.html
+++ b/chalmers/lma017/lma017_13/index.html
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@@ -602,7 +602,7 @@ <h3 id="example-3">Example</h3>
 $$</p>
 <p>$$
 y_0 = \dfrac{\dfrac{10^5}{5} \cdot 2 \cdot 2}{\dfrac{10^4}{4} \cdot 2 \cdot 2} = \ldots = \boxed{8}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_12" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 12 - Change of variables </div> </a> <a href="/chalmers/lma017/lma017_14" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 14 - Curves </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_12" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 12 - Change of variables </div> </a> <a href="/chalmers/lma017/lma017_14" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 14 - Curves </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -348,7 +348,7 @@ <h3 id="example-1">Example</h3>
 $$</p>
 <p>$$
 z(t) = \dfrac{\pi}{2} + t \dfrac{1}{\sqrt{5}} = \boxed{\dfrac{\pi}{2} + \dfrac{t}{\sqrt{5}}}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_13" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 13 - The Jacobian </div> </a> <a href="/chalmers/lma017/lma017_15" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 15 - Line integrals </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_13" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 13 - The Jacobian </div> </a> <a href="/chalmers/lma017/lma017_15" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 15 - Line integrals </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -409,7 +409,7 @@ <h3 id="line-integrals-with-three-variables">Line integrals with three variables
 $$</p>
 <p>$$
 \int_C f(x, y, z)\ ds = \int_a^b f(x(t), y(t), z(t)) \sqrt{x^\prime(t)^2 + y^\prime(t)^2 + z^\prime(t)^2}\ dt
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_14" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 14 - Curves </div> </a> <a href="/chalmers/lma017/lma017_16" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 16 - Vector fields </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_14" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 14 - Curves </div> </a> <a href="/chalmers/lma017/lma017_16" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 16 - Vector fields </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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diff --git a/chalmers/lma017/lma017_16/index.html b/chalmers/lma017/lma017_16/index.html
index 626fa16c..1af35a0f 100644
--- a/chalmers/lma017/lma017_16/index.html
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10.5C5.067 10.5 3.5 8.933 3.5 7ZM9.96544 11.0261C9.13578 11.6382 8.11014 12 7 12C4.23858 12 2 9.76142 2 7C2 4.23858 4.23858 2 7 2C9.76142 2 12 4.23858 12 7C12 8.11014 11.6382 9.13578 11.0261 9.96544L14.0303 12.9697L14.5607 13.5L13.5 14.5607L12.9697 14.0303L9.96544 11.0261Z" fill="currentColor"></path> </svg>
@@ -325,7 +325,7 @@ <h3 id="example-3">Example</h3>
 $$</p>
 <p>$$
 \boxed{\dfrac{5}{7} + \dfrac{1}{4}}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_15" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 15 - Line integrals </div> </a> <a href="/chalmers/lma017/lma017_17" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 17 - Gradient theorem </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_15" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 15 - Line integrals </div> </a> <a href="/chalmers/lma017/lma017_17" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 17 - Gradient theorem </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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index 9797fcb8..f6887c9d 100644
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@@ -406,7 +406,7 @@ <h3 id="conservation-of-energy">Conservation of energy</h3>
 <p>$$
 \boxed{K_E(b) + P_E(b) = K_E(a) + P_E(a)}
 $$</p>
-<p>Which is the law of conservation of energy!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_16" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 16 - Vector fields </div> </a> <a href="/chalmers/lma017/lma017_18" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 18 - Green&#39;s Theorem </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>Which is the law of conservation of energy!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_16" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 16 - Vector fields </div> </a> <a href="/chalmers/lma017/lma017_18" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 18 - Green&#39;s Theorem </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -364,7 +364,7 @@ <h3 id="example-5">Example</h3>
 \vec{r}{u, v} = \langle 2 cos(u), 2 sin(u), v \rangle \ | \ 0 \leq u \leq 2\pi, 0 \leq v \leq 1
 $$</p>
 <p>Plot:
-<img src="/images/school/cyl.png#center" alt=""></p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_17" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 17 - Gradient theorem </div> </a> <a href="/chalmers/lma017/lma017_19" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 19 - Surface integrals </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<img src="/images/school/cyl.png#center" alt=""></p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_17" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 17 - Gradient theorem </div> </a> <a href="/chalmers/lma017/lma017_19" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 19 - Surface integrals </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -400,7 +400,7 @@ <h3 id="example-3">Example</h3>
 <p>$$
 \dfrac{1}{8} \left[ \left(\dfrac{2 \cdot 18^{\frac{3}{2}}}{3} \right) - \left(\dfrac{2 \cdot 2^{\frac{3}{2}}}{3} \right) \right]
 $$</p>
-<p>Good enough :]</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_18" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 18 - Green&#39;s Theorem </div> </a> <a href="/chalmers/lma017/lma017_20" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 20 - Divergence and Stokes&#39; Theorem </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>Good enough :]</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_18" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 18 - Green&#39;s Theorem </div> </a> <a href="/chalmers/lma017/lma017_20" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 20 - Divergence and Stokes&#39; Theorem </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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index b8ae3d60..4113f524 100644
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@@ -385,7 +385,7 @@ <h4 id="examples">Examples</h4>
 f_z(x, y, z) = x^2 - 35yz^4
 $$</p>
 <h3 id="summary">Summary</h3>
-<p>As we have seen continuity is quite similar when dealing with functions of several variables. The <em>partial</em> derivate of functions of several variables are also quite trivial since we treat the other variables as constants!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Functions of several variables </div> </a> <a href="/chalmers/lma017/lma017_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Higher partial derivatives </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>As we have seen continuity is quite similar when dealing with functions of several variables. The <em>partial</em> derivate of functions of several variables are also quite trivial since we treat the other variables as constants!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Functions of several variables </div> </a> <a href="/chalmers/lma017/lma017_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Higher partial derivatives </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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index e52521de..51c81b38 100644
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@@ -374,7 +374,7 @@ <h3 id="example-2">Example</h3>
 $$</p>
 <p>$$
 \int_0^{2\pi} 0 = \boxed{0}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_19" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 19 - Surface integrals </div> </a> <a href="/chalmers/lma017/lma017_summary" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 21 - Summary </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_19" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 19 - Surface integrals </div> </a> <a href="/chalmers/lma017/lma017_summary" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 21 - Summary </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -408,7 +408,7 @@ <h3 id="differentiability">Differentiability</h3>
 <p>Where:
 $$
 \varepsilon_1 = \varepsilon_1(\Delta x, \Delta y), \varepsilon_2 = \varepsilon_2(\Delta x, \Delta y)
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Continuity &amp; partial derivatives. </div> </a> <a href="/chalmers/lma017/lma017_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Chain rule </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Continuity &amp; partial derivatives. </div> </a> <a href="/chalmers/lma017/lma017_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Chain rule </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -430,7 +430,7 @@ <h4 id="example-3">Example</h4>
 <p>Find $\dfrac{\partial z}{\partial y}$, given $x^3 + y^3 + z^3 + 6xyz - 1 = 0$
 $$
 \dfrac{\partial z}{\partial y} = -\dfrac{F_y}{F_z} = - \dfrac{3y^2 + 6xz}{3z^2 + 6xy} = - \dfrac{y^2 + 2xz}{z^2 + 2xy}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Higher partial derivatives </div> </a> <a href="/chalmers/lma017/lma017_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Directional derivatives </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Higher partial derivatives </div> </a> <a href="/chalmers/lma017/lma017_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Directional derivatives </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -453,7 +453,7 @@ <h3 id="gradient-and-level-curves">Gradient and level curves</h3>
 $$</p>
 <p>Where $k$ is just any constant. For each point $(x_0, y_0)$, $\nabla f(x_0, y_0)$ is orthogonal to the level curve that contains $(x_0, y_0)$</p>
 <h4 id="explanation">Explanation</h4>
-<p>We already know that the shortest way up the mountain is to go in the direction of the gradient. On the other hand, the shortest way is to go from level curve to level curve as fast as possible. But shortest way between two lines is the perpendicular way!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Chain rule </div> </a> <a href="/chalmers/lma017/lma017_6" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Maximum and minimum values </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>We already know that the shortest way up the mountain is to go in the direction of the gradient. On the other hand, the shortest way is to go from level curve to level curve as fast as possible. But shortest way between two lines is the perpendicular way!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Chain rule </div> </a> <a href="/chalmers/lma017/lma017_6" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Maximum and minimum values </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -365,7 +365,7 @@ <h4 id="example-2">Example</h4>
 D(1, 1) = 128 \ | \ \text{local minimum} \newline
 D(-1, -1) = 128 \ | \ \text{local minimum} \newline
 \end{cases}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Directional derivatives </div> </a> <a href="/chalmers/lma017/lma017_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Absolute max and min values </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -392,7 +392,7 @@ <h4 id="example">Example</h4>
 $$
 f_{min} = 0 \newline
 f_{max} = 9
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Maximum and minimum values </div> </a> <a href="/chalmers/lma017/lma017_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Lagrange multipliers </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Maximum and minimum values </div> </a> <a href="/chalmers/lma017/lma017_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Lagrange multipliers </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -477,7 +477,7 @@ <h3 id="example-1">Example</h3>
 \end{cases}
 $$</p>
 <p>Now, we could plug these values into our $d$ function, however we can intuitively see which point is closest and furthest.</p>
-<p>Case 1 is the closest and case 2 is the furthest.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Absolute max and min values </div> </a> <a href="/chalmers/lma017/lma017_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Double and triple integrals </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>Case 1 is the closest and case 2 is the furthest.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Absolute max and min values </div> </a> <a href="/chalmers/lma017/lma017_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Double and triple integrals </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -409,7 +409,7 @@ <h3 id="example-2">Example</h3>
 $$</p>
 <p>$$
 -\left( \dfrac{sin(2y)}{2} - sin(y)\right) \bigg\rvert_{y = 0}^{y = \pi} = \ldots = \boxed{0}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Lagrange multipliers </div> </a> <a href="/chalmers/lma017/lma017_10" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - General regions (1) </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Lagrange multipliers </div> </a> <a href="/chalmers/lma017/lma017_10" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - General regions (1) </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -617,7 +617,7 @@ <h3 id="stokes-theorem">Stokes Theorem</h3>
 <p>If $S \subset \mathbb{R}^3$ is a surface, surrounded by a simple, closed curve in $\mathbb{R}^3$. Then:
 $$
 \int_C \vec{F} \cdot dr = \iint_S curl\ F\ dS
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_20" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 20 - Divergence and Stokes&#39; Theorem </div> </a> <div class="invisible"></div> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/lma017/lma017_20" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 20 - Divergence and Stokes&#39; Theorem </div> </a> <div class="invisible"></div> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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-</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/chalmers/ssy081/ssy081_summary" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 10 - Summary </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ssy081/ssy081_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Laplace transform </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ssy081/ssy081_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Signal reconstruction </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ssy081/ssy081_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Nyquist-Shannon sampling theorem </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ssy081/ssy081_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Fourier Transform </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ssy081/ssy081_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Fourier series </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ssy081/ssy081_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Differential equation models </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ssy081/ssy081_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Convolution </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ssy081/ssy081_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - System properties &amp; LTI </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ssy081/ssy081" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Signals </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/chalmers/ssy081/ssy081_summary" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 10 - Summary </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ssy081/ssy081_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Laplace transform </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ssy081/ssy081_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Signal reconstruction </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ssy081/ssy081_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Nyquist-Shannon sampling theorem </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ssy081/ssy081_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Fourier Transform </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ssy081/ssy081_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Fourier series </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ssy081/ssy081_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Differential equation models </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ssy081/ssy081_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Convolution </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ssy081/ssy081_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - System properties &amp; LTI </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/ssy081/ssy081" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - 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@@ -525,7 +525,7 @@ <h3 id="discrete-time">Discrete time</h3>
 
 
 
-<table><thead><tr><th align="center">Operation</th><th align="center">Continuous</th><th align="center">Discrete</th></tr></thead><tbody><tr><td align="center">DC</td><td align="center">$f(t) \to A + f(t)$</td><td align="center"> $f[k] \to A + f[k]$</td></tr><tr><td align="center">Amplitude scaling</td><td align="center">$f(t) \to Af(t)$</td><td align="center">$f[k] \to Af[k]$</td></tr><tr><td align="center">Time scaling</td><td align="center">$f(t) \to f(at)$</td><td align="center">$ f[k] \to f[nk]$</td></tr><tr><td align="center">Reflection</td><td align="center">$f(t) \to f(-t)$</td><td align="center">$f[k] \to f[-k]$</td></tr><tr><td align="center">Time shift</td><td align="center">$f(t) \to f(t \pm t_0)$</td><td align="center">$f[k] \to f[k \pm n_0]$</td></tr></tbody></table> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/chalmers/ssy081/ssy081_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - System properties &amp; LTI </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<table><thead><tr><th align="center">Operation</th><th align="center">Continuous</th><th align="center">Discrete</th></tr></thead><tbody><tr><td align="center">DC</td><td align="center">$f(t) \to A + f(t)$</td><td align="center"> $f[k] \to A + f[k]$</td></tr><tr><td align="center">Amplitude scaling</td><td align="center">$f(t) \to Af(t)$</td><td align="center">$f[k] \to Af[k]$</td></tr><tr><td align="center">Time scaling</td><td align="center">$f(t) \to f(at)$</td><td align="center">$ f[k] \to f[nk]$</td></tr><tr><td align="center">Reflection</td><td align="center">$f(t) \to f(-t)$</td><td align="center">$f[k] \to f[-k]$</td></tr><tr><td align="center">Time shift</td><td align="center">$f(t) \to f(t \pm t_0)$</td><td align="center">$f[k] \to f[k \pm n_0]$</td></tr></tbody></table> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/chalmers/ssy081/ssy081_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - System properties &amp; LTI </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -316,7 +316,7 @@ <h4 id="example-4">Example</h4>
 y(t) = x^2(t) \ | \ \text{\textbf{not} invertible!}
 $$</p>
 <h3 id="lti">LTI</h3>
-<p>Now, LTI, as we defined earlier, are system that are both liner and time time-invariant!. We’ll see why these are important later on!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ssy081/ssy081" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Signals </div> </a> <a href="/chalmers/ssy081/ssy081_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Convolution </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>Now, LTI, as we defined earlier, are system that are both liner and time time-invariant!. We’ll see why these are important later on!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ssy081/ssy081" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Signals </div> </a> <a href="/chalmers/ssy081/ssy081_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Convolution </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -342,7 +342,7 @@ <h4 id="invertibility">Invertibility</h4>
 h(t) * h_i(t) = \delta(t)
 $$</p>
 <h3 id="remark">Remark</h3>
-<p>As always, all of these also apply for discrete-time as well, just sum instead of an integral.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ssy081/ssy081_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - System properties &amp; LTI </div> </a> <a href="/chalmers/ssy081/ssy081_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Differential equation models </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>As always, all of these also apply for discrete-time as well, just sum instead of an integral.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ssy081/ssy081_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - System properties &amp; LTI </div> </a> <a href="/chalmers/ssy081/ssy081_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Differential equation models </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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index 38bd15a8..50d06cca 100644
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@@ -315,7 +315,7 @@ <h4 id="example">Example</h4>
 $$</p>
 <p>$$
 y_0(t) = c_1 e^-t + c_2 e^{-2t}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ssy081/ssy081_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Convolution </div> </a> <a href="/chalmers/ssy081/ssy081_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Fourier series </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ssy081/ssy081_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Convolution </div> </a> <a href="/chalmers/ssy081/ssy081_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Fourier series </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -408,7 +408,7 @@ <h3 id="exponential-fourier-series">Exponential Fourier series</h3>
 <p>In an even more compact form:
 $$
 f(t) = \sum_{-\infty}^{\infty} D_n e^{jn\omega_0 t}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ssy081/ssy081_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Differential equation models </div> </a> <a href="/chalmers/ssy081/ssy081_6" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Fourier Transform </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ssy081/ssy081_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Differential equation models </div> </a> <a href="/chalmers/ssy081/ssy081_6" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Fourier Transform </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -358,7 +358,7 @@ <h3 id="does-the-fourier-transform-always-exist">Does the Fourier transform alwa
 <p>The Fourier transform exist, if:
 $$
 \int_{-\infty}^{\infty} |f(t)|\ dt &#x3C; \infty
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ssy081/ssy081_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Fourier series </div> </a> <a href="/chalmers/ssy081/ssy081_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Nyquist-Shannon sampling theorem </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ssy081/ssy081_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Fourier series </div> </a> <a href="/chalmers/ssy081/ssy081_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Nyquist-Shannon sampling theorem </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -341,7 +341,7 @@ <h3 id="proof">Proof</h3>
 2\pi \mathcal{F} > 2(2 \pi B) \newline
 2\pi \mathcal{F} > 4 \pi B \newline
 \boxed{\mathcal{F} > 2B}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ssy081/ssy081_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Fourier Transform </div> </a> <a href="/chalmers/ssy081/ssy081_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Signal reconstruction </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ssy081/ssy081_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Fourier Transform </div> </a> <a href="/chalmers/ssy081/ssy081_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Signal reconstruction </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -254,7 +254,7 @@ <h3 id="interpolation">Interpolation</h3>
 <p>We can also interpolate using the sinc function.
 $$
 \sum_k f(kT)\ sinc(2\pi Bt - k\pi)
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ssy081/ssy081_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Nyquist-Shannon sampling theorem </div> </a> <a href="/chalmers/ssy081/ssy081_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Laplace transform </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ssy081/ssy081_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Nyquist-Shannon sampling theorem </div> </a> <a href="/chalmers/ssy081/ssy081_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Laplace transform </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -336,7 +336,7 @@ <h4 id="convolution">Convolution</h4>
 <p>Frequency convolution
 $$
 f_1(t) f_2(t) = \dfrac{1}{2\pi j} \left[F_1(s) * F_2(s)\right]
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ssy081/ssy081_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Signal reconstruction </div> </a> <a href="/chalmers/ssy081/ssy081_summary" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Summary </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ssy081/ssy081_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Signal reconstruction </div> </a> <a href="/chalmers/ssy081/ssy081_summary" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Summary </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -443,7 +443,7 @@ <h3 id="definition-1">Definition</h3>
 <p>$$
 F(s) = \int_0^{\infty} f(t)e^{-st}\ dt \newline
 F(s) = \mathcal{L}[f(t)]
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ssy081/ssy081_9" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Laplace transform </div> </a> <div class="invisible"></div> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/ssy081/ssy081_9" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Laplace transform </div> </a> <div class="invisible"></div> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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-</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/chalmers/tda384/tda384_10" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 10 - Parallel linked lists </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/tda384/tda384_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Parallelizing computations </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/tda384/tda384_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Synchronization problems (2) </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/tda384/tda384_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 &amp; 7 - Message-Passing Concurrency </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/tda384/tda384_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Monitors </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/tda384/tda384_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Synchronization problems (1) </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/tda384/tda384_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Models of concurrency </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/tda384/tda384_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Races, Locks, and Semaphores </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/tda384/tda384" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Introduction </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/chalmers/tda384/tda384_10" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 10 - Parallel linked lists </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/tda384/tda384_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Parallelizing computations </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/tda384/tda384_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Synchronization problems (2) </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/tda384/tda384_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 &amp; 7 - Message-Passing Concurrency </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/tda384/tda384_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Monitors </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/tda384/tda384_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Synchronization problems (1) </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/tda384/tda384_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Models of concurrency </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/tda384/tda384_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Races, Locks, and Semaphores </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/chalmers/tda384/tda384" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - 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@@ -377,7 +377,7 @@ <h1 id="traces">Traces</h1>
 <p>So different <em>traces</em> lead to different results in the program.</p>
 <h1 id="conclusion">Conclusion</h1>
 <p>This concludes this first part in this series, we’ve only looked at the pure basics and terminology here.
-In the next part we’ll cover races, locks and semaphores, which are the first real concurrency principles we’ll look at.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/chalmers/tda384/tda384_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Races, Locks, and Semaphores </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+In the next part we’ll cover races, locks and semaphores, which are the first real concurrency principles we’ll look at.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/chalmers/tda384/tda384_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Races, Locks, and Semaphores </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -885,7 +885,7 @@ <h3 id="when-to-lock-and-not">When to lock and not</h3>
 <li>
 <p><code>LockFreeSet</code> works well when locking is quite expensive</p>
 </li>
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@@ -340,7 +340,7 @@ <h3 id="barriers">Barriers</h3>
 <span class="line"><span>// code after barrier</span></span></code></pre>
 <p>We can see that this ensures they wait for each other at this point at the program.</p>
 <h3 id="summary">Summary</h3>
-<p>This concludes this part - races, locks and semaphores are an important part in solving concurrent problems that can occur.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/tda384/tda384" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Introduction </div> </a> <a href="/chalmers/tda384/tda384_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Models of concurrency </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>This concludes this part - races, locks and semaphores are an important part in solving concurrent problems that can occur.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/tda384/tda384" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Introduction </div> </a> <a href="/chalmers/tda384/tda384_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Models of concurrency </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -491,7 +491,7 @@ <h3 id="implementation">Implementation</h3>
 <h3 id="summary">Summary</h3>
 <p>This concludes this part, there was a lot of info in this one - but writing and implementing
 good concurrent programs from scratch is a pain. I even left out how to implement a semaphore from scratch.</p>
-<p>I’ll maybe update and put it in later :).</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/tda384/tda384_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Races, Locks, and Semaphores </div> </a> <a href="/chalmers/tda384/tda384_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Synchronization problems (1) </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>I’ll maybe update and put it in later :).</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/tda384/tda384_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Races, Locks, and Semaphores </div> </a> <a href="/chalmers/tda384/tda384_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Synchronization problems (1) </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -745,7 +745,7 @@ <h3 id="readers-writers">Readers-Writers</h3>
 <h3 id="summary">Summary</h3>
 <p>A looong part, but as we can see, all solution uses locks and semaphores.
 When writing solutions to concurrent programs, we will always need to use these.
-To lock and gain exclusive access.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/tda384/tda384_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Models of concurrency </div> </a> <a href="/chalmers/tda384/tda384_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Monitors </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+To lock and gain exclusive access.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/tda384/tda384_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Models of concurrency </div> </a> <a href="/chalmers/tda384/tda384_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Monitors </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -554,7 +554,7 @@ <h3 id="summary">Summary</h3>
 <li>For complex synchronization patterns, nested monitor calls will be complicated.</li>
 </ul>
 </li>
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 <span class="line"><span></span></span>
 <span class="line"><span>    % wait for response, and return it:</span></span>
-<span class="line"><span>    receive {response, Ref, Result} -> Result end.</span></span></code></pre> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/tda384/tda384_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Monitors </div> </a> <a href="/chalmers/tda384/tda384_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Synchronization problems (2) </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<span class="line"><span>    receive {response, Ref, Result} -> Result end.</span></span></code></pre> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/tda384/tda384_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Monitors </div> </a> <a href="/chalmers/tda384/tda384_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Synchronization problems (2) </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -665,7 +665,7 @@ <h3 id="dining-philosophers">Dining Philosophers</h3>
 <span class="line"><span>        % 1-based indexes</span></span>
 <span class="line"><span>        Right = lists:nth(1+(I rem N), Forks),</span></span>
 <span class="line"><span>        philosopher(#forks{left=Left, right=Right}, Waiter)</span></span>
-<span class="line"><span>    end) || I &#x3C;- Ids].</span></span></code></pre> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/tda384/tda384_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 &amp; 7 - Message-Passing Concurrency </div> </a> <a href="/chalmers/tda384/tda384_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Parallelizing computations </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<span class="line"><span>    end) || I &#x3C;- Ids].</span></span></code></pre> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/tda384/tda384_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 &amp; 7 - Message-Passing Concurrency </div> </a> <a href="/chalmers/tda384/tda384_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Parallelizing computations </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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index 8c4a466b..14c00970 100644
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@@ -414,7 +414,7 @@ <h3 id="pools-and-work-stealing">Pools and work stealing</h3>
 each task</p>
 <p>With stealing, the pool may even send all tasks to one default thread, letting other
 idle threads steal directly from it, simplifying the pool and reducing the
-synchronization costs it incurs</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/tda384/tda384_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Synchronization problems (2) </div> </a> <a href="/chalmers/tda384/tda384_10" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Parallel linked lists </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+synchronization costs it incurs</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/tda384/tda384_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Synchronization problems (2) </div> </a> <a href="/chalmers/tda384/tda384_10" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Parallel linked lists </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -325,7 +325,7 @@ <h3 id="latent-heat">Latent Heat</h3>
 <p>Where $L$ - specific latent heat for a particular substance [J/kg]</p>
 <h3 id="conclusion">Conclusion</h3>
 <p>This was everything for the first part of the thermodynamics,
-in the next time we’ll looking into how gases behave and why they are so important for thermodynamics.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/chalmers/tif085/tif085_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Lecture 2 </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -435,7 +435,7 @@ <h3 id="thermal-efficiency">Thermal Efficiency</h3>
 $$</p>
 <p>Thermal efficiency can also sometimes be denoted as $\eta$.</p>
 <h3 id="conclusion">Conclusion</h3>
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@@ -336,7 +336,7 @@ <h3 id="combing-1st-and-2nd-law">Combing 1st and 2nd Law</h3>
 $$</p>
 <p>So now we can utilize something called ‘TS’ diagrams instead of always using ‘PV’ diagrams. In TS diagrams it’s really easy to calculate Q.</p>
 <h3 id="conclusion">Conclusion</h3>
-<p>This concludes this part and the series as a whole (probably). I really enjoyed writing and will probably continuing writing all my notes here, since I learn <strong>a lot</strong> doing this.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/tif085/tif085_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Lecture 2 </div> </a> <a href="/chalmers/tif085/tif085_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Mechanical Waves </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>This concludes this part and the series as a whole (probably). I really enjoyed writing and will probably continuing writing all my notes here, since I learn <strong>a lot</strong> doing this.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/tif085/tif085_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Lecture 2 </div> </a> <a href="/chalmers/tif085/tif085_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Mechanical Waves </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -428,7 +428,7 @@ <h4 id="if-both-are-moving">If both are moving</h4>
 f_L = \frac{V + V_L}{V + V_S}\ f_S
 $$</p>
 <h3 id="conclusion">Conclusion</h3>
-<p>This was it for this part - quite short, waves are a quite natural phenomena so a lot of things comes from intuition. In the next part we’ll begin to cover light waves!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/tif085/tif085_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Lecture 3 </div> </a> <a href="/chalmers/tif085/tif085_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Light waves </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>This was it for this part - quite short, waves are a quite natural phenomena so a lot of things comes from intuition. In the next part we’ll begin to cover light waves!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/tif085/tif085_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Lecture 3 </div> </a> <a href="/chalmers/tif085/tif085_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Light waves </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -347,7 +347,7 @@ <h3 id="optical-resolution">Optical resolution</h3>
 $$</p>
 <h3 id="conclusion">Conclusion</h3>
 <p>This was it for light waves - yes a very short part since a lot of the intuition and proofs are visual and I can’t be bothered to put pictures of these at the moment :)</p>
-<p>So take the formulas and go! :)</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/tif085/tif085_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Mechanical Waves </div> </a> <div class="invisible"></div> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>So take the formulas and go! :)</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/chalmers/tif085/tif085_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Mechanical Waves </div> </a> <div class="invisible"></div> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -267,7 +267,7 @@ <h3 id="definition-of-a-control-system">Definition of a Control System</h3>
 <strong>Figure 4:</strong> Room temperature control system example.</p>
 <h3 id="linear-and-nonlinear-systems">Linear and Nonlinear Systems</h3>
 <p>Control systems can be classified as <em>linear</em> or <em>nonlinear</em> based on the mathematical models that describe their behavior.</p>
-<p>We’ll exactly define what makes a system linear or nonlinear in a later part of this course.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/cityu/bme3105/bme3105_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - System Modelling </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -348,7 +348,7 @@ <h4 id="superposition-principle">Superposition Principle</h4>
 <p>Additivity,
 $$
 x_1(t) + x_2(t) \rightarrow y_1(t) + y_2(t)
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/bme3105/bme3105" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Introduction </div> </a> <a href="/cityu/bme3105/bme3105_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Modelling in Frequency Domain </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/bme3105/bme3105" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Introduction </div> </a> <a href="/cityu/bme3105/bme3105_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Modelling in Frequency Domain </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -431,7 +431,7 @@ <h3 id="summary">Summary</h3>
 <li>Laplace transform is a powerful tool to convert differential equations into algebraic equations.</li>
 <li>Transfer functions are the relationship between the Laplace transform of the input and output signals of a system.</li>
 <li>Transfer functions can be combined in series or parallel to form more complex systems.</li>
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@@ -444,7 +444,7 @@ <h3 id="transient-response-of-higher-order-system">Transient Response of Higher
 <p>so that the time domain response is of the form,
 $$
 x_0(t) = 1 + \sum_{r = 1}^N B_r e^{\sigma_r t} + \sum_{c = 1}^N B_c e^{\sigma_c t} \sin(\omega_c t)
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/bme3105/bme3105_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Modelling in Frequency Domain </div> </a> <a href="/cityu/bme3105/bme3105_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Stability </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -638,7 +638,7 @@ <h5 id="example">Example</h5>
 <table><thead><tr><th align="center">Label</th><th align="center">First Column</th><th align="center">$\epsilon = +$</th><th align="center">$\epsilon = -$</th></tr></thead><tbody><tr><td align="center">$s^5$</td><td align="center">1</td><td align="center">+</td><td align="center">+</td></tr><tr><td align="center">$s^4$</td><td align="center">2</td><td align="center">+</td><td align="center">+</td></tr><tr><td align="center">$s^3$</td><td align="center">$\epsilon$</td><td align="center">+</td><td align="center">-</td></tr><tr><td align="center">$s^2$</td><td align="center">$\frac{6 \epsilon - 7}{\epsilon}$</td><td align="center">-</td><td align="center">+</td></tr><tr><td align="center">$s^1$</td><td align="center">$\frac{42 \epsilon - 49 - 6 \epsilon^2}{12 \epsilon - 14}$</td><td align="center">+</td><td align="center">+</td></tr><tr><td align="center">$s^0$</td><td align="center">3</td><td align="center">+</td><td align="center">+</td></tr></tbody></table>
 <p>We have two sign changes in the first column, therefore the system is <strong>unstable</strong>.</p>
 <h3 id="conclusion">Conclusion</h3>
-<p>The Routh-Hurwitz criterion is a powerful tool for determining the stability of a system without having to find the poles of the closed-loop system.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/bme3105/bme3105_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Time Respone </div> </a> <a href="/cityu/bme3105/bme3105_6" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - State Space Approach </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>The Routh-Hurwitz criterion is a powerful tool for determining the stability of a system without having to find the poles of the closed-loop system.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/bme3105/bme3105_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Time Respone </div> </a> <a href="/cityu/bme3105/bme3105_6" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - State Space Approach </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -615,7 +615,7 @@ <h3 id="transfer-function-of-siso-systems">Transfer Function of SISO Systems</h3
 <p>where $\gamma(s)$ is the greatest common divisor of $\beta(s)$ and $\alpha(s)$.
 Thus, $\beta_d(s)$ and $\alpha_d(s)$ are coprime (the greatest common divisor of them is a constant).</p>
 <p>The roots of $\alpha_d(s)$ are called the poles of $P(s)$ and the roots of $\beta_d(s)$ are called the zeros of $P(s)$.</p>
-<p>All poles of $P(s)$ are the eigenvalues of $F$, but some eigenvalues of $F$ may not be the poles of $P(s)$!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/bme3105/bme3105_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Stability </div> </a> <a href="/cityu/bme3105/bme3105_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - State Space Realization </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>All poles of $P(s)$ are the eigenvalues of $F$, but some eigenvalues of $F$ may not be the poles of $P(s)$!</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/bme3105/bme3105_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Stability </div> </a> <a href="/cityu/bme3105/bme3105_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - State Space Realization </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -703,7 +703,7 @@ <h3 id="properties-and-remarks">Properties and Remarks</h3>
 <li>$\{A_c, B_c, C_c\}$ is always controllable, but may not be observable. But if $C_c(sI - A_c)^{-1} B_c$ is irreducible, then $\{A_c, B_c, C_c\}$ is also observable.</li>
 <li>$\{A_o, B_o, C_o\}$ is always observable, but may not be controllable. But if $C_o(sI - A_o)^{-1} B_o$ is irreducible, then $\{A_o, B_o, C_o\}$ is also controllable.</li>
 <li>Define $C(F, G) = \begin{bmatrix} G &#x26; FG &#x26; \ldots &#x26; F^{n - 1}G \end{bmatrix}$ and call it the controllability matrix, and $O(H, F) = \begin{bmatrix} H \newline HF \newline \vdots \newline HF^{n - 1} \end{bmatrix}$ and call it the observability matrix.</li>
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--- a/cityu/bme3105/bme3105_8/index.html
+++ b/cityu/bme3105/bme3105_8/index.html
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@@ -705,7 +705,7 @@ <h5 id="solution">Solution</h5>
 <p>Thus, the control law is,</p>
 <p>$$
 u = -Kx + Mr = -3x_1 - 4x_2 + 4r
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/bme3105/bme3105_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - State Space Realization </div> </a> <a href="/cityu/bme3105/bme3105_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Discrete Systems </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/bme3105/bme3105_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - State Space Realization </div> </a> <a href="/cityu/bme3105/bme3105_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Discrete Systems </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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index f7b7814a..e7daf6b7 100644
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@@ -596,7 +596,7 @@ <h5 id="matched-pole-zero-mpz-method">Matched Pole-Zero (MPZ) Method</h5>
 <p>Thus,</p>
 <p>$$
 D(z) = 0.1 \frac{z - 0.82}{z - 0.135}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/bme3105/bme3105_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Stability and Controller Design </div> </a> <div class="invisible"></div> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/bme3105/bme3105_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Stability and Controller Design </div> </a> <div class="invisible"></div> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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diff --git a/cityu/bme3105/index.html b/cityu/bme3105/index.html
index f062e5e9..fa7b2492 100644
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 </button> </nav> </div> </div> </header> <main>  <div class="mx-auto max-w-screen-sm px-3"> <h1 class="mb-6 text-3xl font-bold"> Biomedical Systems And Control (BME3105)
-</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/cityu/bme3105/bme3105_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Discrete Systems </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/bme3105/bme3105_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Stability and Controller Design </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/bme3105/bme3105_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - State Space Realization </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/bme3105/bme3105_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - State Space Approach </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/bme3105/bme3105_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Stability </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/bme3105/bme3105_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Time Respone </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/bme3105/bme3105_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Modelling in Frequency Domain </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/bme3105/bme3105_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - System Modelling </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/bme3105/bme3105" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Introduction </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/cityu/bme3105/bme3105_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Discrete Systems </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/bme3105/bme3105_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Stability and Controller Design </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/bme3105/bme3105_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - State Space Realization </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/bme3105/bme3105_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - State Space Approach </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/bme3105/bme3105_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Stability </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/bme3105/bme3105_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Time Respone </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/bme3105/bme3105_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Modelling in Frequency Domain </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/bme3105/bme3105_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - System Modelling </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/bme3105/bme3105" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Introduction </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -576,7 +576,7 @@ <h3 id="bayes-classifier-summary">Bayes Classifier Summary</h3>
 </ol>
 <p>For classification, given a new sample $\mathbf{x}^\star$, calculate the likelihood $p(\mathbf{x}^\star | y = c)$ for each class $c$.
 Pick the class $c$ with the largest posterior probability $p(y = c | \mathbf{x}^\star)$.</p>
-<p>Equivalently, use $p(\mathbf{x}^\star | y = c)p(y = c)$ or $\log p(\mathbf{x}^\star | y = c) + \log p(y = c)$.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/cityu/cs4487/cs4487_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Generative VS. Discriminative Models </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>Equivalently, use $p(\mathbf{x}^\star | y = c)p(y = c)$ or $\log p(\mathbf{x}^\star | y = c) + \log p(y = c)$.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/cityu/cs4487/cs4487_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Generative VS. Discriminative Models </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -779,7 +779,7 @@ <h3 id="summary">Summary</h3>
 <li>Choosing Hyperparameters</li>
 </ul>
 </li>
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@@ -610,7 +610,7 @@ <h4 id="deep-image-structure-and-texture-similarity-dists">Deep Image Structure
 <h3 id="summary">Summary</h3>
 <p>Advances of deep learning has been driven by the ImageNet competition.</p>
 <p>As depth increases, need to have a smart architecture design to make training more effective.</p>
-<p>Deep learning also beigns to dominate low-level vision, e.g., image denoising, deblurring, super-resolution, compression etc.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/cs4487/cs4487_10" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Neural Networks and Deep Learning Part 2 </div> </a> <div class="invisible"></div> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>Deep learning also beigns to dominate low-level vision, e.g., image denoising, deblurring, super-resolution, compression etc.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/cs4487/cs4487_10" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Neural Networks and Deep Learning Part 2 </div> </a> <div class="invisible"></div> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -606,7 +606,7 @@ <h4 id="logistic-regression-summary">Logistic Regression Summary</h4>
 +1, &#x26; f(\mathbf{x}^\star) > 0 \newline
 -1, &#x26; \text{otherwise}
 \end{cases}
-$$</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/cs4487/cs4487" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Introduction </div> </a> <a href="/cityu/cs4487/cs4487_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Optimization and Convexity </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -741,7 +741,7 @@ <h3 id="summary-svm">Summary: SVM</h3>
 <li>Decision surface can only be linear.</li>
 </ul>
 </li>
-</ul> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/cs4487/cs4487_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Generative VS. Discriminative Models </div> </a> <a href="/cityu/cs4487/cs4487_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Duality and SVM </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+</ul> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/cs4487/cs4487_2" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Generative VS. Discriminative Models </div> </a> <a href="/cityu/cs4487/cs4487_4" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Duality and SVM </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -899,7 +899,7 @@ <h3 id="which-classifier-is-best">Which Classifier is Best?</h3>
 <blockquote>
 <p>If an algorithm performs well on a certain class of problems then it necessarily pays for that with degraded performance on the set of all remaining problems.</p>
 </blockquote>
-<p>In other words, there is <strong>no best</strong> classifier for all tasks. The best classifier depends on the particular problem.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/cs4487/cs4487_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Optimization and Convexity </div> </a> <a href="/cityu/cs4487/cs4487_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Regression </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>In other words, there is <strong>no best</strong> classifier for all tasks. The best classifier depends on the particular problem.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/cs4487/cs4487_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Optimization and Convexity </div> </a> <a href="/cityu/cs4487/cs4487_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Regression </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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index 3c5f048b..94958c17 100644
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@@ -525,7 +525,7 @@ <h3 id="linear-regression-summary">Linear Regression Summary</h3>
 </ul>
 </li>
 <li>All fail when output $y$ <strong>non-linearly</strong> depends on input features $\mathbf{x}$.</li>
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@@ -682,7 +682,7 @@ <h4 id="trade-offs">Trade-Offs</h4>
 <p>The original $K$-means algorithm performs hard assignments during clustering, and implicitly assumes all clusters will have an equal number of points assigned as well as a unit covariance matrix.</p>
 <p>GMM for clustering relaxes all of these assumptions. The objective still has multiple local optima.</p>
 <p>EM can also be used with any component densities/distributions to customize the model to a given data set.</p>
-<p>As with $K$-means, intialization is important for GMM.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/cs4487/cs4487_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Regression </div> </a> <a href="/cityu/cs4487/cs4487_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - The Expectation Maximization Algorithm &amp; Linear Dimensionality Reduction </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>As with $K$-means, intialization is important for GMM.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/cs4487/cs4487_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Regression </div> </a> <a href="/cityu/cs4487/cs4487_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - The Expectation Maximization Algorithm &amp; Linear Dimensionality Reduction </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -565,7 +565,7 @@ <h4 id="eckart-young-mirsky-theorem">Eckart-Young-Mirsky Theorem</h4>
 \Vert \mathbf{X} - \mathbf{Y}^{\star} \Vert_F^2 = \min \{\Vert \mathbf{X} - \mathbf{Y} \Vert_F^2; \mathbf{Y} \in \mathbb{R}^{M \times N}, \text{rank} \mathbf{Y} \leq K\}
 $$</p>
 </blockquote>
-<p>SVD provdies a unique solution to minimum Frobenius norm linear dimensionality reduction.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/cs4487/cs4487_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Robust, Non-Linear Regression and Clustering </div> </a> <a href="/cityu/cs4487/cs4487_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Principal Component Analysis </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -558,7 +558,7 @@ <h3 id="summary">Summary</h3>
 </ul>
 <p>Using RBF kernel, KPCA can split the data into clusters.</p>
 <p>Kernel PCA can provide an effective pre-processing step for clustering methods as well as linear classification and regression methods.</p>
-<p>However, exact compuation of kernel PCA can be expensive because the size of the matrix to be decomposed is $M \times M$.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/cs4487/cs4487_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - The Expectation Maximization Algorithm &amp; Linear Dimensionality Reduction </div> </a> <a href="/cityu/cs4487/cs4487_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Neural Networks and Deep Learning </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 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Linear Dimensionality Reduction </div> </a> <a href="/cityu/cs4487/cs4487_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - Neural Networks and Deep Learning </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 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@@ -715,7 +715,7 @@ <h3 id="summary">Summary</h3>
 <li>Sensitive to initialization, learning rate, training algorithm.</li>
 </ul>
 </li>
-</ul> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/cs4487/cs4487_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Principal Component Analysis </div> </a> <a href="/cityu/cs4487/cs4487_10" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Neural Networks and Deep Learning Part 2 </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+</ul> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/cs4487/cs4487_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Principal Component Analysis </div> </a> <a href="/cityu/cs4487/cs4487_10" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Neural Networks and Deep Learning Part 2 </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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 </button> </nav> </div> </div> </header> <main>  <div class="mx-auto max-w-screen-sm px-3"> <h1 class="mb-6 text-3xl font-bold"> Machine Learning (CS4487)
-</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/cityu/cs4487/cs4487_11" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 11 - High-Level and Low-Level Vision Applications </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487_10" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 10 - Neural Networks and Deep Learning Part 2 </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Neural Networks and Deep Learning </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Principal Component Analysis </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - The Expectation Maximization Algorithm &amp; Linear Dimensionality Reduction </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Robust, Non-Linear Regression and Clustering </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Regression </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Duality and SVM </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Optimization and Convexity </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Generative VS. Discriminative Models </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Introduction </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/cityu/cs4487/cs4487_11" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 11 - High-Level and Low-Level Vision Applications </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487_10" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 10 - Neural Networks and Deep Learning Part 2 </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - Neural Networks and Deep Learning </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Principal Component Analysis </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - The Expectation Maximization Algorithm &amp; Linear Dimensionality Reduction </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Robust, Non-Linear Regression and Clustering </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Regression </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Duality and SVM </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Optimization and Convexity </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Generative VS. Discriminative Models </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/cs4487/cs4487" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Introduction </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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-</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/cityu/is2021/is2021_10" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 10 - Future trends of Big Data </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/is2021/is2021_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - NoSQL Data Management for Big Data </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/is2021/is2021_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Data Governance for BDA – Data Policies &amp; Processes </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/is2021/is2021_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Developing a Strategy for Integrating Big Data Analytics into the Enterprise </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/is2021/is2021_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Achieving Organizational Alignment for Big Data Analytics </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/is2021/is2021_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Developing Big Data Applications </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/is2021/is2021_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Big Data Tools and Techniques </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/is2021/is2021_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - High-Performance Applications </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/is2021/is2021_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Business Drivers for Big Data Analytics &amp; its related Business Problems </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/is2021/is2021" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Evolution of Data Management </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/cityu/is2021/is2021_10" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 10 - Future trends of Big Data </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/is2021/is2021_9" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 9 - NoSQL Data Management for Big Data </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/is2021/is2021_8" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 8 - Data Governance for BDA – Data Policies &amp; Processes </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/is2021/is2021_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Developing a Strategy for Integrating Big Data Analytics into the Enterprise </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/is2021/is2021_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Achieving Organizational Alignment for Big Data Analytics </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/is2021/is2021_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Developing Big Data Applications </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/is2021/is2021_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Big Data Tools and Techniques </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/is2021/is2021_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - High-Performance Applications </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/is2021/is2021_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Business Drivers for Big Data Analytics &amp; its related Business Problems </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/is2021/is2021" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - 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@@ -312,7 +312,7 @@ <h4 id="big-data">Big Data</h4>
 <li>Value</li>
 </ul>
 <p><img src="/images/cityu/IS2021/BD.jpg" alt="">
-<strong>Figure 4.</strong> The Three Vs of Big Data</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/cityu/is2021/is2021_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Business Drivers for Big Data Analytics &amp; its related Business Problems </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<strong>Figure 4.</strong> The Three Vs of Big Data</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/cityu/is2021/is2021_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Business Drivers for Big Data Analytics &amp; its related Business Problems </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -313,7 +313,7 @@ <h3 id="summary">Summary</h3>
 <li>Handled by NoSQL and Hadoop.</li>
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@@ -359,7 +359,7 @@ <h3 id="adoption-criteria-of-big-data-applications">Adoption Criteria of Big Dat
 <li>Because of reduced data dependencies</li>
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@@ -403,7 +403,7 @@ <h3 id="considering-platform-alternatives">Considering Platform Alternatives</h3
 <p>Benefits of using hardware appliances for big data center on engineering and integration.</p>
 <p>They are engineered for high-performance reporting and analytics, yet have a flexible architecture allowing integrated components to be configured to meet specific application needs.</p>
 <p>Benefit of using software appliances is that they can take advantage of low-cost commodity hardware components.</p>
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@@ -298,7 +298,7 @@ <h3 id="mapreduce">MapReduce</h3>
 As the sequence of the name <strong>MapReduce</strong> implies, the reduce job is always performed after the map job.</p>
 <p>MapReduce execution environment employs a master/Slave execution model, in which on master node (<strong>JobTracker</strong>) manages a pool of slave computing resources (<strong>TaskTrackers</strong>) that are called upon to do the actual work.</p>
 <p>The role of <strong>JobTracker</strong> is to manage the resources with some specific responsibilities, including managing <strong>TaskTrackers</strong>, continually monitoring their accessibility, availability and different aspects of job management.</p>
-<p>Role of <strong>TaskTracker</strong> is much simpler - wait for a task assignment, initiate and execute the requested task, and provide status back to the <strong>JobTracker</strong> periodically.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/is2021/is2021_3" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - High-Performance Applications </div> </a> <a href="/cityu/is2021/is2021_5" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Developing Big Data Applications </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 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@@ -471,7 +471,7 @@ <h5 id="comparison-of-hadoop-and-hpcc">Comparison of Hadoop and HPCC</h5>
 <p>In fact, each of the ECL programming constructs can be executed in parallel.</p>
 <h3 id="testing">Testing</h3>
 <p>This milestone is a must for the whole application development project because there may have some unfound errors in systems analysis, design and implementation milestones.</p>
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@@ -323,7 +323,7 @@ <h3 id="roles-of-organizational-alignment">Roles of Organizational Alignment</h3
 <h3 id="conclusion">Conclusion</h3>
 <p>The <strong>alignment of business and technology</strong> is critical to the success of any big data analytics project. The <strong>business process owners</strong> must be engaged in the process to ensure that the technology is being applied to the right problems and that the results are being communicated in a way that is meaningful to the business.</p>
 <p>The <strong>technical infrastructure innovators</strong> must be engaged to ensure that the technology is being applied in a way that is scalable, reliable, and secure. The <strong>application developers</strong> must be engaged to ensure that the technology is being applied in a way that is efficient, maintainable, and extensible.</p>
-<p>The <strong>enterprise architects</strong> must be engaged to ensure that the technology is being applied in a way that is aligned with the overall architecture of the organization. The <strong>program managers</strong> must be engaged to ensure that the technology is being applied in a way that is aligned with the overall goals of the organization and that the project is being managed in a way that is efficient and effective.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/is2021/is2021_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Developing Big Data Applications </div> </a> <a href="/cityu/is2021/is2021_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Developing a Strategy for Integrating Big Data Analytics into the Enterprise </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 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+<p>The <strong>enterprise architects</strong> must be engaged to ensure that the technology is being applied in a way that is aligned with the overall architecture of the organization. The <strong>program managers</strong> must be engaged to ensure that the technology is being applied in a way that is aligned with the overall goals of the organization and that the project is being managed in a way that is efficient and effective.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/is2021/is2021_5" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 5 - Developing Big Data Applications </div> </a> <a href="/cityu/is2021/is2021_7" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Developing a Strategy for Integrating Big Data Analytics into the Enterprise </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 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@@ -275,7 +275,7 @@ <h4 id="promote-data-reuserepurpose">Promote Data Reuse/Repurpose</h4>
 <p>Different analyses will employ a variety of data sources, implying the potential need to use <strong>the same</strong> datasets multiple times in different ways.</p>
 <h4 id="institute-proper-levels-of-oversight-and-governance">Institute Proper Levels of Oversight and Governance</h4>
 <p>Grey areas: navigating the boundary between speculative application development; assessing pilot projects and when successful and then transitioning those pilots into the mainstream.</p>
-<p>The above cannot be done without some oversight and governance which will properly direct the alignment of speculative development with achieving buisness goals in relation to the collected business requirments.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/is2021/is2021_6" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Achieving Organizational Alignment for Big Data Analytics </div> </a> <a href="/cityu/is2021/is2021_8" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Data Governance for BDA – Data Policies &amp; 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@@ -353,7 +353,7 @@ <h5 id="example">Example</h5>
 <p>A large online retailer want to drive increased sales through relationship analysis and look at sales correlations.</p>
 <p>When processing millions of transactions a day, a minimal number of inconsistencies, incomplete records or errors are likely to be irrelevant.</p>
 <p>Should incorrect values be an impediment to the analysis and making changes does not significantly alter the data from its original form other than in a positive and an expected way, data enhancement and enrichment may be a reasonable alternative.</p>
-<p>If address locations may be incomplete or even incorrect, standardizing an address’s format and applying corrections is a consistent way to improve the data.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/is2021/is2021_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Developing a Strategy for Integrating Big Data Analytics into the Enterprise </div> </a> <a href="/cityu/is2021/is2021_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - NoSQL Data Management for Big Data </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 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+<p>If address locations may be incomplete or even incorrect, standardizing an address’s format and applying corrections is a consistent way to improve the data.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/is2021/is2021_7" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 7 - Developing a Strategy for Integrating Big Data Analytics into the Enterprise </div> </a> <a href="/cityu/is2021/is2021_9" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 9 - NoSQL Data Management for Big Data </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 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@@ -332,7 +332,7 @@ <h3 id="nosql-vs-sql">NoSQL VS. SQL</h3>
 
 <table><thead><tr><th></th><th>NoSQL</th><th>SQL</th></tr></thead><tbody><tr><td>Intended Purpose</td><td>Specific use case</td><td>General purpose</td></tr><tr><td>API</td><td>SQL not required</td><td>SQL required</td></tr><tr><td>Data Model</td><td>Various, depending on NoSQL database type</td><td>Tables with fixed rows and columns</td></tr><tr><td>Schema</td><td>Flexible</td><td>Rigid</td></tr><tr><td>Scalability</td><td>Horizontal scale out</td><td>Vertical scale up</td></tr><tr><td>Data Integrity</td><td>BASE</td><td>ACID</td></tr></tbody></table>
 <p>BASE: <strong>B</strong>asically <strong>A</strong>vailable, <strong>S</strong>oft state, <strong>E</strong>ventual consistency.</p>
-<p>ACID: <strong>A</strong>tomicity, <strong>C</strong>onsistency, <strong>I</strong>solation, <strong>D</strong>urability.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/is2021/is2021_8" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 8 - Data Governance for BDA – Data Policies &amp; Processes </div> </a> <a href="/cityu/is2021/is2021_10" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 10 - Future trends of Big Data </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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-</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/cityu/ma3518/ma3518_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Multiple Linear Regression </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/ma3518/ma3518_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Simple Linear Regression </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/ma3518/ma3518_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Confidence Interval and Hypothesis Testing </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/ma3518/ma3518_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Basic Statistical Concepts and Tools </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/ma3518/ma3518" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Introduction to R </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/cityu/ma3518/ma3518_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Multiple Linear Regression </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/ma3518/ma3518_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - 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@@ -515,7 +515,7 @@ <h3 id="basic-probability">Basic Probability</h3>
 <p>And for other distributions, for example the Binomial distribution,</p>
 <pre class="astro-code css-variables" style="background-color:var(--astro-code-background);color:var(--astro-code-foreground); overflow-x: auto;" tabindex="0" data-language="r"><code><span class="line"><span style="color:var(--astro-code-token-keyword)">></span><span style="color:var(--astro-code-token-function)"> dbinom</span><span style="color:var(--astro-code-foreground)">(</span><span style="color:var(--astro-code-token-constant)">0</span><span style="color:var(--astro-code-token-keyword)">:</span><span style="color:var(--astro-code-token-constant)">5</span><span style="color:var(--astro-code-foreground)">, size</span><span style="color:var(--astro-code-token-keyword)">=</span><span style="color:var(--astro-code-token-constant)">5</span><span style="color:var(--astro-code-foreground)">, prob</span><span style="color:var(--astro-code-token-keyword)">=</span><span style="color:var(--astro-code-token-constant)">0.5</span><span style="color:var(--astro-code-foreground)">)</span></span>
 <span class="line"><span style="color:var(--astro-code-foreground)">[</span><span style="color:var(--astro-code-token-constant)">1</span><span style="color:var(--astro-code-foreground)">] </span><span style="color:var(--astro-code-token-constant)">0.03125</span><span style="color:var(--astro-code-token-constant)"> 0.15625</span><span style="color:var(--astro-code-token-constant)"> 0.31250</span><span style="color:var(--astro-code-token-constant)"> 0.31250</span><span style="color:var(--astro-code-token-constant)"> 0.15625</span><span style="color:var(--astro-code-token-constant)"> 0.03125</span></span></code></pre>
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@@ -436,7 +436,7 @@ <h4 id="students-t-distribution">Student’s t-Distribution</h4>
 $$</p>
 <p>In R, we can generate random variables from a t-distribution using the <code>rt()</code> function.
 For cauchy, we can use the <code>rcauchy()</code> function.</p>
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@@ -828,7 +828,7 @@ <h3 id="inferences-for-ratio-of-variancestest-of-equality-of-variances">Inferenc
 $$
 P(F > f) = 1 - P(F(n_1 - 1, n_2 - 1) \leq f) \newline
 P(F &#x3C; f) = P(F(n_1 - 1, n_2 - 1) \leq f)
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@@ -594,7 +594,7 @@ <h4 id="non-constant-variance">Non-constant Variance</h4>
 <li>Fit a linear regression model $y_i = \beta_0 + \beta_1 x_i + e_i$.</li>
 <li>Estimate $g^{-1}$ by plotting $\hat{y_i} = \hat{\beta}_0 + \hat{\beta}_1 x_i$ against $x_i$.</li>
 <li>Mathematically, we <em>minimize</em> $\sum_i (\hat{y_i} - \alpha_0 - \alpha_1 \psi(y_i, \lambda))^2$ over $(\alpha_0, \alpha_1, \lambda)$.</li>
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@@ -669,7 +669,7 @@ <h4 id="collinearity-of-predictors">Collinearity of Predictors</h4>
 <ol>
 <li>Do nothing but be careful of interpretation.</li>
 <li>Remove highly correlated variables (keep only one of them).</li>
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-</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/cityu/mne3115/mne3115_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Thermal Actuators and Piezoresistivity </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/mne3115/mne3115_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Elasticity </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/mne3115/mne3115_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Fabrication Techniques </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/mne3115/mne3115_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Etching </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/mne3115/mne3115_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Thin Film Growth and Deposition </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/mne3115/mne3115_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Photolithography </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/mne3115/mne3115" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Introduction </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+</h1> <aside data-pagefind-ignore> <div class="space-y-10"> <div class="space-y-4"> <section class="animate space-y-4"> <div> <ul class="not-prose flex flex-col gap-4"> <li> <a href="/cityu/mne3115/mne3115_7" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 7 - Thermal Actuators and Piezoresistivity </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/mne3115/mne3115_6" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 6 - Elasticity </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/mne3115/mne3115_5" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 5 - Fabrication Techniques </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/mne3115/mne3115_4" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 4 - Etching </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/mne3115/mne3115_3" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 3 - Thin Film Growth and Deposition </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/mne3115/mne3115_2" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 2 - Photolithography </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li><li> <a href="/cityu/mne3115/mne3115" class="not-prose group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pr-10 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <div class="flex flex-1 flex-col truncate"> <div class="font-semibold"> Part 1 - Introduction </div>  <div class="text-sm">  </div> </div> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> </a> </li> </ul> </div> </section> </div> </div> </aside> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -257,7 +257,7 @@ <h3 id="mems-fabrication">MEMS Fabrication</h3>
 However, MEMS face manufacturing challenges at very small scales.</p>
 <h3 id="summary">Summary</h3>
 <p>In summary, MEMS enables the miniaturization of electromechanical devices down to the micrometer scale, unlocking new applications across multiple domains from consumer electronics to biomedical systems.
-The future of MEMS lies in continued miniaturization and integration of more functionality on-chip.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/cityu/mne3115/mne3115_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Photolithography </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+The future of MEMS lies in continued miniaturization and integration of more functionality on-chip.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/cityu/mne3115/mne3115_2" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 2 - Photolithography </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -473,7 +473,7 @@ <h3 id="artifacts-in-exposure">Artifacts in Exposure</h3>
 <p>Front to back surface (substrate reflections in resists can create standing wave patterns that alter scallop the resist edges.</p>
 <h3 id="artifacts-in-development">Artifacts in Development</h3>
 <p>Quantify line &#x26; gap width, line and gap width may vary, but spatial period = layout.</p>
-<p>Under/over development can cause non-ideal cross-sections.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/mne3115/mne3115" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 1 - Introduction </div> </a> <a href="/cityu/mne3115/mne3115_3" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 3 - Thin Film Growth and Deposition </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -409,7 +409,7 @@ <h5 id="properties-of-sputtering">Properties of Sputtering</h5>
 <li>Higher impurity due to the low vacuum.</li>
 </ul>
 </li>
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diff --git a/cityu/mne3115/mne3115_4/index.html b/cityu/mne3115/mne3115_4/index.html
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@@ -447,7 +447,7 @@ <h4 id="thermocompression-bonding">Thermocompression Bonding</h4>
 <ul>
 <li>Bonding temperature 380 to 450$^\circ$C.</li>
 <li>Applied force above 15 - 30 MPa.</li>
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diff --git a/cityu/mne3115/mne3115_5/index.html b/cityu/mne3115/mne3115_5/index.html
index a52c3345..92c01e5c 100644
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@@ -370,7 +370,7 @@ <h4 id="antistick">Antistick</h4>
 This is crucial for UV NIL. Otherwise, the resist will stick to the template and not the wafer.</p>
 <h3 id="imprinting-in-presence-of-a-particle-contamination">Imprinting in Presence of a Particle (Contamination)</h3>
 <p>If there is contamination on the wafer or resist itself, the imprinting process will be affected.</p>
-<p>If there is contamination under the wafer, the wafer may even crack.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/mne3115/mne3115_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Etching </div> </a> <a href="/cityu/mne3115/mne3115_6" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Elasticity </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>If there is contamination under the wafer, the wafer may even crack.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/cityu/mne3115/mne3115_4" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 4 - Etching </div> </a> <a href="/cityu/mne3115/mne3115_6" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Part 6 - Elasticity </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -393,7 +393,7 @@ <h4 id="applications-of-membrane-structures">Applications of membrane structures
 </li>
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@@ -455,7 +455,7 @@ <h3 id="analysis-of-accelerometer">Analysis of Accelerometer</h3>
 <p>Assuming the gauge factor is $G$, the change in resistance is,</p>
 <p>$$
 \frac{\Delta R}{R} = G \varepsilon_{\text{max}} = \frac{6GF\left(l + \frac{L}{2}\right)}{Ewt^3} = \left(\frac{6GF\left(l + \frac{L}{2}\right)}{Ew^2t^2}\right) a.
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@@ -232,7 +232,7 @@
                                 the way from classical ML to SOTA models.
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Mostrant al seu lloc resultats per [DIFFERENT_TERM]",search_suggestion:"No es van trobar resultats per [SEARCH_TERM]. Proveu una de les cerques seg\xFCents:",searching:"Cercant [SEARCH_TERM]..."},hr={thanks_to:cr,comments:_r,direction:fr,strings:dr};var At={};y(At,{comments:()=>pr,default:()=>Rr,direction:()=>gr,strings:()=>Er,thanks_to:()=>mr});var mr="Dalibor Hon <https://github.com/dallyh>",pr="",gr="ltr",Er={placeholder:"Hledat",clear_search:"Smazat",load_more:"Na\u010D\xEDst dal\u0161\xED v\xFDsledky",search_label:"Prohledat tuto str\xE1nku",filters_label:"Filtry",zero_results:"\u017D\xE1dn\xE9 v\xFDsledky pro [SEARCH_TERM]",many_results:"[COUNT] v\xFDsledk\u016F pro [SEARCH_TERM]",one_result:"[COUNT] v\xFDsledek pro [SEARCH_TERM]",alt_search:"\u017D\xE1dn\xE9 v\xFDsledky pro [SEARCH_TERM]. Zobrazuj\xED se v\xFDsledky pro [DIFFERENT_TERM]",search_suggestion:"\u017D\xE1dn\xE9 v\xFDsledky pro [SEARCH_TERM]. Souvisej\xEDc\xED v\xFDsledky hled\xE1n\xED:",searching:"Hled\xE1m [SEARCH_TERM]..."},Rr={thanks_to:mr,comments:pr,direction:gr,strings:Er};var vt={};y(vt,{comments:()=>Tr,default:()=>Sr,direction:()=>Cr,strings:()=>kr,thanks_to:()=>br});var br="Jonas Smedegaard <dr@jones.dk>",Tr="",Cr="ltr",kr={placeholder:"S\xF8g",clear_search:"Nulstil",load_more:"Indl\xE6s flere resultater",search_label:"S\xF8g p\xE5 dette website",filters_label:"Filtre",zero_results:"Ingen resultater for [SEARCH_TERM]",many_results:"[COUNT] resultater for [SEARCH_TERM]",one_result:"[COUNT] resultat for [SEARCH_TERM]",alt_search:"Ingen resultater for [SEARCH_TERM]. Viser resultater for [DIFFERENT_TERM] i stedet",search_suggestion:"Ingen resultater for [SEARCH_TERM]. Pr\xF8v et af disse s\xF8geord i stedet:",searching:"S\xF8ger efter [SEARCH_TERM]..."},Sr={thanks_to:br,comments:Tr,direction:Cr,strings:kr};var wt={};y(wt,{comments:()=>Mr,default:()=>wr,direction:()=>Ar,strings:()=>vr,thanks_to:()=>yr});var yr="Jan Claasen <jan@cloudcannon.com>",Mr="",Ar="ltr",vr={placeholder:"Suche",clear_search:"L\xF6schen",load_more:"Mehr Ergebnisse laden",search_label:"Suche diese Seite",filters_label:"Filter",zero_results:"Keine Ergebnisse f\xFCr [SEARCH_TERM]",many_results:"[COUNT] Ergebnisse f\xFCr [SEARCH_TERM]",one_result:"[COUNT] Ergebnis f\xFCr [SEARCH_TERM]",alt_search:"Keine Ergebnisse f\xFCr [SEARCH_TERM]. Stattdessen werden Ergebnisse f\xFCr [DIFFERENT_TERM] angezeigt",search_suggestion:"Keine Ergebnisse f\xFCr [SEARCH_TERM]. Versuchen Sie eine der folgenden Suchen:",searching:"Suche f\xFCr [SEARCH_TERM]"},wr={thanks_to:yr,comments:Mr,direction:Ar,strings:vr};var Ht={};y(Ht,{comments:()=>Fr,default:()=>jr,direction:()=>Nr,strings:()=>Or,thanks_to:()=>Hr});var Hr="Liam Bigelow <liam@cloudcannon.com>",Fr="",Nr="ltr",Or={placeholder:"Search",clear_search:"Clear",load_more:"Load more results",search_label:"Search this site",filters_label:"Filters",zero_results:"No results for [SEARCH_TERM]",many_results:"[COUNT] results for [SEARCH_TERM]",one_result:"[COUNT] result for [SEARCH_TERM]",alt_search:"No results for [SEARCH_TERM]. Showing results for [DIFFERENT_TERM] instead",search_suggestion:"No results for [SEARCH_TERM]. Try one of the following searches:",searching:"Searching for [SEARCH_TERM]..."},jr={thanks_to:Hr,comments:Fr,direction:Nr,strings:Or};var Ft={};y(Ft,{comments:()=>Ur,default:()=>Pr,direction:()=>Dr,strings:()=>Ir,thanks_to:()=>zr});var zr="Pablo Villaverde <https://github.com/pvillaverde>",Ur="",Dr="ltr",Ir={placeholder:"Buscar",clear_search:"Limpiar",load_more:"Ver m\xE1s resultados",search_label:"Buscar en este sitio",filters_label:"Filtros",zero_results:"No se encontraron resultados para [SEARCH_TERM]",many_results:"[COUNT] resultados encontrados para [SEARCH_TERM]",one_result:"[COUNT] resultado encontrado para [SEARCH_TERM]",alt_search:"No se encontraron resultados para [SEARCH_TERM]. Mostrando en su lugar resultados para [DIFFERENT_TERM]",search_suggestion:"No se encontraron resultados para [SEARCH_TERM]. Prueba una de las siguientes b\xFAsquedas:",searching:"Buscando [SEARCH_TERM]..."},Pr={thanks_to:zr,comments:Ur,direction:Dr,strings:Ir};var Nt={};y(Nt,{comments:()=>qr,default:()=>Wr,direction:()=>Br,strings:()=>Vr,thanks_to:()=>Lr});var Lr="Ali Khaleqi Yekta <https://yekta.dev>",qr="",Br="rtl",Vr={placeholder:"\u062C\u0633\u062A\u062C\u0648",clear_search:"\u067E\u0627\u06A9\u0633\u0627\u0632\u06CC",load_more:"\u0628\u0627\u0631\u06AF\u0630\u0627\u0631\u06CC \u0646\u062A\u0627\u06CC\u062C \u0628\u06CC\u0634\u062A\u0631",search_label:"\u062C\u0633\u062A\u062C\u0648 \u062F\u0631 \u0633\u0627\u06CC\u062A",filters_label:"\u0641\u06CC\u0644\u062A\u0631\u0647\u0627",zero_results:"\u0646\u062A\u06CC\u062C\u0647\u200C\u0627\u06CC \u0628\u0631\u0627\u06CC [SEARCH_TERM] \u06CC\u0627\u0641\u062A \u0646\u0634\u062F",many_results:"[COUNT] \u0646\u062A\u06CC\u062C\u0647 \u0628\u0631\u0627\u06CC [SEARCH_TERM] \u06CC\u0627\u0641\u062A \u0634\u062F",one_result:"[COUNT] \u0646\u062A\u06CC\u062C\u0647 \u0628\u0631\u0627\u06CC [SEARCH_TERM] \u06CC\u0627\u0641\u062A \u0634\u062F",alt_search:"\u0646\u062A\u06CC\u062C\u0647\u200C\u0627\u06CC \u0628\u0631\u0627\u06CC [SEARCH_TERM] \u06CC\u0627\u0641\u062A \u0646\u0634\u062F. \u062F\u0631 \u0639\u0648\u0636 \u0646\u062A\u0627\u06CC\u062C \u0628\u0631\u0627\u06CC [DIFFERENT_TERM] \u0646\u0645\u0627\u06CC\u0634 \u062F\u0627\u062F\u0647 \u0645\u06CC\u200C\u0634\u0648\u062F",search_suggestion:"\u0646\u062A\u06CC\u062C\u0647\u200C\u0627\u06CC \u0628\u0631\u0627\u06CC [SEARCH_TERM] \u06CC\u0627\u0641\u062A \u0646\u0634\u062F. \u06CC\u06A9\u06CC \u0627\u0632 \u062C\u0633\u062A\u062C\u0648\u0647\u0627\u06CC \u0632\u06CC\u0631 \u0631\u0627 \u0627\u0645\u062A\u062D\u0627\u0646 \u06A9\u0646\u06CC\u062F:",searching:"\u062F\u0631 \u062D\u0627\u0644 \u062C\u0633\u062A\u062C\u0648\u06CC [SEARCH_TERM]..."},Wr={thanks_to:Lr,comments:qr,direction:Br,strings:Vr};var Ot={};y(Ot,{comments:()=>Kr,default:()=>Zr,direction:()=>Jr,strings:()=>Yr,thanks_to:()=>Gr});var Gr="Valtteri Laitinen <dev@valtlai.fi>",Kr="",Jr="ltr",Yr={placeholder:"Haku",clear_search:"Tyhjenn\xE4",load_more:"Lataa lis\xE4\xE4 tuloksia",search_label:"Hae t\xE4lt\xE4 sivustolta",filters_label:"Suodattimet",zero_results:"Ei tuloksia haulle [SEARCH_TERM]",many_results:"[COUNT] tulosta haulle [SEARCH_TERM]",one_result:"[COUNT] tulos haulle [SEARCH_TERM]",alt_search:"Ei tuloksia haulle [SEARCH_TERM]. N\xE4ytet\xE4\xE4n tulokset sen sijaan haulle [DIFFERENT_TERM]",search_suggestion:"Ei tuloksia haulle [SEARCH_TERM]. Kokeile jotain seuraavista:",searching:"Haetaan [SEARCH_TERM]..."},Zr={thanks_to:Gr,comments:Kr,direction:Jr,strings:Yr};var jt={};y(jt,{comments:()=>Qr,default:()=>el,direction:()=>xr,strings:()=>$r,thanks_to:()=>Xr});var Xr="Nicolas Friedli <nicolas@theologique.ch>",Qr="",xr="ltr",$r={placeholder:"Rechercher",clear_search:"Nettoyer",load_more:"Charger plus de r\xE9sultats",search_label:"Recherche sur ce site",filters_label:"Filtres",zero_results:"Pas de r\xE9sultat pour [SEARCH_TERM]",many_results:"[COUNT] r\xE9sultats pour [SEARCH_TERM]",one_result:"[COUNT] r\xE9sultat pour [SEARCH_TERM]",alt_search:"Pas de r\xE9sultat pour [SEARCH_TERM]. Montre les r\xE9sultats pour [DIFFERENT_TERM] \xE0 la place",search_suggestion:"Pas de r\xE9sultat pour [SEARCH_TERM]. Essayer une des recherches suivantes:",searching:"Recherche [SEARCH_TERM]..."},el={thanks_to:Xr,comments:Qr,direction:xr,strings:$r};var zt={};y(zt,{comments:()=>nl,default:()=>ll,direction:()=>sl,strings:()=>rl,thanks_to:()=>tl});var tl="Pablo Villaverde <https://github.com/pvillaverde>",nl="",sl="ltr",rl={placeholder:"Buscar",clear_search:"Limpar",load_more:"Ver m\xE1is resultados",search_label:"Buscar neste sitio",filters_label:"Filtros",zero_results:"Non se atoparon resultados para [SEARCH_TERM]",many_results:"[COUNT] resultados atopados para [SEARCH_TERM]",one_result:"[COUNT] resultado atopado para [SEARCH_TERM]",alt_search:"Non se atoparon resultados para [SEARCH_TERM]. Amosando no seu lugar resultados para [DIFFERENT_TERM]",search_suggestion:"Non se atoparon resultados para [SEARCH_TERM]. Probe unha das seguintes pesquisas:",searching:"Buscando [SEARCH_TERM]..."},ll={thanks_to:tl,comments:nl,direction:sl,strings:rl};var Ut={};y(Ut,{comments:()=>al,default:()=>cl,direction:()=>ol,strings:()=>ul,thanks_to:()=>il});var il="Nir Tamir <nirtamir2@gmail.com>",al="",ol="rtl",ul={placeholder:"\u05D7\u05D9\u05E4\u05D5\u05E9",clear_search:"\u05E0\u05D9\u05E7\u05D5\u05D9",load_more:"\u05E2\u05D5\u05D3 \u05EA\u05D5\u05E6\u05D0\u05D5\u05EA",search_label:"\u05D7\u05D9\u05E4\u05D5\u05E9 \u05D1\u05D0\u05EA\u05E8 \u05D6\u05D4",filters_label:"\u05DE\u05E1\u05E0\u05E0\u05D9\u05DD",zero_results:"\u05DC\u05D0 \u05E0\u05DE\u05E6\u05D0\u05D5 \u05EA\u05D5\u05E6\u05D0\u05D5\u05EA \u05E2\u05D1\u05D5\u05E8 [SEARCH_TERM]",many_results:"\u05E0\u05DE\u05E6\u05D0\u05D5 [COUNT] \u05EA\u05D5\u05E6\u05D0\u05D5\u05EA \u05E2\u05D1\u05D5\u05E8 [SEARCH_TERM]",one_result:"\u05E0\u05DE\u05E6\u05D0\u05D4 \u05EA\u05D5\u05E6\u05D0\u05D4 \u05D0\u05D7\u05EA \u05E2\u05D1\u05D5\u05E8 [SEARCH_TERM]",alt_search:"\u05DC\u05D0 \u05E0\u05DE\u05E6\u05D0\u05D5 \u05EA\u05D5\u05E6\u05D0\u05D5\u05EA \u05E2\u05D1\u05D5\u05E8 [SEARCH_TERM]. \u05DE\u05D5\u05E6\u05D2\u05D5\u05EA \u05EA\u05D5\u05E6\u05D0\u05D5\u05EA \u05E2\u05D1\u05D5\u05E8 [DIFFERENT_TERM]",search_suggestion:"\u05DC\u05D0 \u05E0\u05DE\u05E6\u05D0\u05D5 \u05EA\u05D5\u05E6\u05D0\u05D5\u05EA \u05E2\u05D1\u05D5\u05E8 [SEARCH_TERM]. \u05E0\u05E1\u05D5 \u05D0\u05D7\u05D3 \u05DE\u05D4\u05D7\u05D9\u05E4\u05D5\u05E9\u05D9\u05DD \u05D4\u05D1\u05D0\u05D9\u05DD:",searching:"\u05DE\u05D7\u05E4\u05E9 \u05D0\u05EA [SEARCH_TERM]..."},cl={thanks_to:il,comments:al,direction:ol,strings:ul};var Dt={};y(Dt,{comments:()=>fl,default:()=>ml,direction:()=>dl,strings:()=>hl,thanks_to:()=>_l});var _l="Amit Yadav <amit@thetechbasket.com>",fl="",dl="ltr",hl={placeholder:"\u0916\u094B\u091C\u0947\u0902",clear_search:"\u0938\u093E\u092B \u0915\u0930\u0947\u0902",load_more:"\u0914\u0930 \u0905\u0927\u093F\u0915 \u092A\u0930\u093F\u0923\u093E\u092E \u0932\u094B\u0921 \u0915\u0930\u0947\u0902",search_label:"\u0907\u0938 \u0938\u093E\u0907\u091F \u092E\u0947\u0902 \u0916\u094B\u091C\u0947\u0902",filters_label:"\u092B\u093C\u093F\u0932\u094D\u091F\u0930",zero_results:"\u0915\u094B\u0908 \u092A\u0930\u093F\u0923\u093E\u092E [SEARCH_TERM] \u0915\u0947 \u0932\u093F\u090F \u0928\u0939\u0940\u0902 \u092E\u093F\u0932\u093E",many_results:"[COUNT] \u092A\u0930\u093F\u0923\u093E\u092E [SEARCH_TERM] \u0915\u0947 \u0932\u093F\u090F \u092E\u093F\u0932\u0947",one_result:"[COUNT] \u092A\u0930\u093F\u0923\u093E\u092E [SEARCH_TERM] \u0915\u0947 \u0932\u093F\u090F \u092E\u093F\u0932\u093E",alt_search:"[SEARCH_TERM] \u0915\u0947 \u0932\u093F\u090F \u0915\u094B\u0908 \u092A\u0930\u093F\u0923\u093E\u092E \u0928\u0939\u0940\u0902 \u092E\u093F\u0932\u093E\u0964 \u0907\u0938\u0915\u0947 \u092C\u091C\u093E\u092F [DIFFERENT_TERM] \u0915\u0947 \u0932\u093F\u090F \u092A\u0930\u093F\u0923\u093E\u092E \u0926\u093F\u0916\u093E \u0930\u0939\u093E \u0939\u0948",search_suggestion:"[SEARCH_TERM] \u0915\u0947 \u0932\u093F\u090F \u0915\u094B\u0908 \u092A\u0930\u093F\u0923\u093E\u092E \u0928\u0939\u0940\u0902 \u092E\u093F\u0932\u093E\u0964 \u0928\u093F\u092E\u094D\u0928\u0932\u093F\u0916\u093F\u0924 \u0916\u094B\u091C\u094B\u0902 \u092E\u0947\u0902 \u0938\u0947 \u0915\u094B\u0908 \u090F\u0915 \u0906\u091C\u093C\u092E\u093E\u090F\u0902:",searching:"[SEARCH_TERM] \u0915\u0940 \u0916\u094B\u091C \u0915\u0940 \u091C\u093E \u0930\u0939\u0940 \u0939\u0948..."},ml={thanks_to:_l,comments:fl,direction:dl,strings:hl};var It={};y(It,{comments:()=>gl,default:()=>bl,direction:()=>El,strings:()=>Rl,thanks_to:()=>pl});var pl="Diomed <https://github.com/diomed>",gl="",El="ltr",Rl={placeholder:"Tra\u017Ei",clear_search:"O\u010Disti",load_more:"U\u010Ditaj vi\u0161e rezultata",search_label:"Pretra\u017Ei ovu stranicu",filters_label:"Filteri",zero_results:"Nema rezultata za [SEARCH_TERM]",many_results:"[COUNT] rezultata za [SEARCH_TERM]",one_result:"[COUNT] rezultat za [SEARCH_TERM]",alt_search:"Nema rezultata za [SEARCH_TERM]. Prikazujem rezultate za [DIFFERENT_TERM]",search_suggestion:"Nema rezultata za [SEARCH_TERM]. Poku\u0161aj s jednom od ovih pretraga:",searching:"Pretra\u017Eujem [SEARCH_TERM]..."},bl={thanks_to:pl,comments:gl,direction:El,strings:Rl};var Pt={};y(Pt,{comments:()=>Cl,default:()=>yl,direction:()=>kl,strings:()=>Sl,thanks_to:()=>Tl});var Tl="Adam Laki <info@adamlaki.com>",Cl="",kl="ltr",Sl={placeholder:"Keres\xE9s",clear_search:"T\xF6rl\xE9s",load_more:"Tov\xE1bbi tal\xE1latok bet\xF6lt\xE9se",search_label:"Keres\xE9s az oldalon",filters_label:"Sz\u0171r\xE9s",zero_results:"Nincs tal\xE1lat a(z) [SEARCH_TERM] kifejez\xE9sre",many_results:"[COUNT] db tal\xE1lat a(z) [SEARCH_TERM] kifejez\xE9sre",one_result:"[COUNT] db tal\xE1lat a(z) [SEARCH_TERM] kifejez\xE9sre",alt_search:"Nincs tal\xE1lat a(z) [SEARCH_TERM] kifejez\xE9sre. Tal\xE1latok mutat\xE1sa ink\xE1bb a(z) [DIFFERENT_TERM] kifejez\xE9sre",search_suggestion:"Nincs tal\xE1lat a(z) [SEARCH_TERM] kifejez\xE9sre. Pr\xF3b\xE1ld meg a k\xF6vetkez\u0151 keres\xE9sek egyik\xE9t:",searching:"Keres\xE9s a(z) [SEARCH_TERM] kifejez\xE9sre..."},yl={thanks_to:Tl,comments:Cl,direction:kl,strings:Sl};var Lt={};y(Lt,{comments:()=>Al,default:()=>Hl,direction:()=>vl,strings:()=>wl,thanks_to:()=>Ml});var Ml="Nixentric",Al="",vl="ltr",wl={placeholder:"Cari",clear_search:"Bersihkan",load_more:"Muat lebih banyak hasil",search_label:"Telusuri situs ini",filters_label:"Filter",zero_results:"[SEARCH_TERM] tidak ditemukan",many_results:"Ditemukan [COUNT] hasil untuk [SEARCH_TERM]",one_result:"Ditemukan [COUNT] hasil untuk [SEARCH_TERM]",alt_search:"[SEARCH_TERM] tidak ditemukan. Menampilkan hasil [DIFFERENT_TERM] sebagai gantinya",search_suggestion:"[SEARCH_TERM] tidak ditemukan. Coba salah satu pencarian berikut ini:",searching:"Mencari [SEARCH_TERM]..."},Hl={thanks_to:Ml,comments:Al,direction:vl,strings:wl};var qt={};y(qt,{comments:()=>Nl,default:()=>zl,direction:()=>Ol,strings:()=>jl,thanks_to:()=>Fl});var Fl="Cosette Bruhns Alonso, Andrew Janco <apjanco@upenn.edu>",Nl="",Ol="ltr",jl={placeholder:"Cerca",clear_search:"Cancella la cronologia",load_more:"Mostra pi\xF9 risultati",search_label:"Cerca nel sito",filters_label:"Filtri di ricerca",zero_results:"Nessun risultato per [SEARCH_TERM]",many_results:"[COUNT] risultati per [SEARCH_TERM]",one_result:"[COUNT] risultato per [SEARCH_TERM]",alt_search:"Nessun risultato per [SEARCH_TERM]. Mostrando risultati per [DIFFERENT_TERM] come alternativa.",search_suggestion:"Nessun risultato per [SEARCH_TERM]. Prova una delle seguenti ricerche:",searching:"Cercando [SEARCH_TERM]..."},zl={thanks_to:Fl,comments:Nl,direction:Ol,strings:jl};var Bt={};y(Bt,{comments:()=>Dl,default:()=>Ll,direction:()=>Il,strings:()=>Pl,thanks_to:()=>Ul});var Ul="Tate",Dl="",Il="ltr",Pl={placeholder:"\u691C\u7D22",clear_search:"\u30AF\u30EA\u30A2",load_more:"\u6B21\u3092\u8AAD\u307F\u8FBC\u3080",search_label:"\u3053\u306E\u30B5\u30A4\u30C8\u3092\u691C\u7D22",filters_label:"\u30D5\u30A3\u30EB\u30BF",zero_results:"[SEARCH_TERM]\u306E\u691C\u7D22\u306B\u4E00\u81F4\u3059\u308B\u60C5\u5831\u306F\u3042\u308A\u307E\u305B\u3093\u3067\u3057\u305F",many_results:"[SEARCH_TERM]\u306E[COUNT]\u4EF6\u306E\u691C\u7D22\u7D50\u679C",one_result:"[SEARCH_TERM]\u306E[COUNT]\u4EF6\u306E\u691C\u7D22\u7D50\u679C",alt_search:"[SEARCH_TERM]\u306E\u691C\u7D22\u306B\u4E00\u81F4\u3059\u308B\u60C5\u5831\u306F\u3042\u308A\u307E\u305B\u3093\u3067\u3057\u305F\u3002[DIFFERENT_TERM]\u306E\u691C\u7D22\u7D50\u679C\u3092\u8868\u793A\u3057\u3066\u3044\u307E\u3059",search_suggestion:"[SEARCH_TERM]\u306E\u691C\u7D22\u306B\u4E00\u81F4\u3059\u308B\u60C5\u5831\u306F\u3042\u308A\u307E\u305B\u3093\u3067\u3057\u305F\u3002\u6B21\u306E\u3044\u305A\u308C\u304B\u306E\u691C\u7D22\u3092\u8A66\u3057\u3066\u304F\u3060\u3055\u3044",searching:"[SEARCH_TERM]\u3092\u691C\u7D22\u3057\u3066\u3044\u307E\u3059"},Ll={thanks_to:Ul,comments:Dl,direction:Il,strings:Pl};var Vt={};y(Vt,{comments:()=>Bl,default:()=>Gl,direction:()=>Vl,strings:()=>Wl,thanks_to:()=>ql});var ql="Seokho Son <https://github.com/seokho-son>",Bl="",Vl="ltr",Wl={placeholder:"\uAC80\uC0C9\uC5B4",clear_search:"\uBE44\uC6B0\uAE30",load_more:"\uAC80\uC0C9 \uACB0\uACFC \uB354 \uBCF4\uAE30",search_label:"\uC0AC\uC774\uD2B8 \uAC80\uC0C9",filters_label:"\uD544\uD130",zero_results:"[SEARCH_TERM]\uC5D0 \uB300\uD55C \uACB0\uACFC \uC5C6\uC74C",many_results:"[SEARCH_TERM]\uC5D0 \uB300\uD55C \uACB0\uACFC [COUNT]\uAC74",one_result:"[SEARCH_TERM]\uC5D0 \uB300\uD55C \uACB0\uACFC [COUNT]\uAC74",alt_search:"[SEARCH_TERM]\uC5D0 \uB300\uD55C \uACB0\uACFC \uC5C6\uC74C. [DIFFERENT_TERM]\uC5D0 \uB300\uD55C \uACB0\uACFC",search_suggestion:"[SEARCH_TERM]\uC5D0 \uB300\uD55C \uACB0\uACFC \uC5C6\uC74C. \uCD94\uCC9C \uAC80\uC0C9\uC5B4: ",searching:"[SEARCH_TERM] \uAC80\uC0C9 \uC911..."},Gl={thanks_to:ql,comments:Bl,direction:Vl,strings:Wl};var Wt={};y(Wt,{comments:()=>Jl,default:()=>Xl,direction:()=>Yl,strings:()=>Zl,thanks_to:()=>Kl});var Kl="",Jl="",Yl="ltr",Zl={placeholder:"Rapu",clear_search:"Whakakore",load_more:"Whakauta \u0113tahi otinga k\u0113",search_label:"Rapu",filters_label:"T\u0101tari",zero_results:"Otinga kore ki [SEARCH_TERM]",many_results:"[COUNT] otinga ki [SEARCH_TERM]",one_result:"[COUNT] otinga ki [SEARCH_TERM]",alt_search:"Otinga kore ki [SEARCH_TERM]. Otinga k\u0113 ki [DIFFERENT_TERM]",search_suggestion:"Otinga kore ki [SEARCH_TERM]. whakam\u0101tau ki ng\u0101 mea atu:",searching:"Rapu ki [SEARCH_TERM]..."},Xl={thanks_to:Kl,comments:Jl,direction:Yl,strings:Zl};var Gt={};y(Gt,{comments:()=>xl,default:()=>ti,direction:()=>$l,strings:()=>ei,thanks_to:()=>Ql});var Ql="Paul van Brouwershaven",xl="",$l="ltr",ei={placeholder:"Zoeken",clear_search:"Reset",load_more:"Meer resultaten laden",search_label:"Doorzoek deze site",filters_label:"Filters",zero_results:"Geen resultaten voor [SEARCH_TERM]",many_results:"[COUNT] resultaten voor [SEARCH_TERM]",one_result:"[COUNT] resultaat voor [SEARCH_TERM]",alt_search:"Geen resultaten voor [SEARCH_TERM]. In plaats daarvan worden resultaten voor [DIFFERENT_TERM] weergegeven",search_suggestion:"Geen resultaten voor [SEARCH_TERM]. Probeer een van de volgende zoekopdrachten:",searching:"Zoeken naar [SEARCH_TERM]..."},ti={thanks_to:Ql,comments:xl,direction:$l,strings:ei};var Kt={};y(Kt,{comments:()=>si,default:()=>ii,direction:()=>ri,strings:()=>li,thanks_to:()=>ni});var ni="Christopher Wingate",si="",ri="ltr",li={placeholder:"S\xF8k",clear_search:"Fjern",load_more:"Last flere resultater",search_label:"S\xF8k p\xE5 denne siden",filters_label:"Filtre",zero_results:"Ingen resultater for [SEARCH_TERM]",many_results:"[COUNT] resultater for [SEARCH_TERM]",one_result:"[COUNT] resultat for [SEARCH_TERM]",alt_search:"Ingen resultater for [SEARCH_TERM]. Viser resultater for [DIFFERENT_TERM] i stedet",search_suggestion:"Ingen resultater for [SEARCH_TERM]. Pr\xF8v en av disse s\xF8keordene i stedet:",searching:"S\xF8ker etter [SEARCH_TERM]"},ii={thanks_to:ni,comments:si,direction:ri,strings:li};var Jt={};y(Jt,{comments:()=>oi,default:()=>_i,direction:()=>ui,strings:()=>ci,thanks_to:()=>ai});var ai="",oi="",ui="ltr",ci={placeholder:"Szukaj",clear_search:"Wyczy\u015B\u0107",load_more:"Za\u0142aduj wi\u0119cej",search_label:"Przeszukaj t\u0119 stron\u0119",filters_label:"Filtry",zero_results:"Brak wynik\xF3w dla [SEARCH_TERM]",many_results:"[COUNT] wynik\xF3w dla [SEARCH_TERM]",one_result:"[COUNT] wynik dla [SEARCH_TERM]",alt_search:"Brak wynik\xF3w dla [SEARCH_TERM]. Wy\u015Bwietlam wyniki dla [DIFFERENT_TERM]",search_suggestion:"Brak wynik\xF3w dla [SEARCH_TERM]. Pokrewne wyniki wyszukiwania:",searching:"Szukam [SEARCH_TERM]..."},_i={thanks_to:ai,comments:oi,direction:ui,strings:ci};var Yt={};y(Yt,{comments:()=>di,default:()=>pi,direction:()=>hi,strings:()=>mi,thanks_to:()=>fi});var fi="Jonatah",di="",hi="ltr",mi={placeholder:"Pesquisar",clear_search:"Limpar",load_more:"Ver mais resultados",search_label:"Pesquisar",filters_label:"Filtros",zero_results:"Nenhum resultado encontrado para [SEARCH_TERM]",many_results:"[COUNT] resultados encontrados para [SEARCH_TERM]",one_result:"[COUNT] resultado encontrado para [SEARCH_TERM]",alt_search:"Nenhum resultado encontrado para [SEARCH_TERM]. Exibindo resultados para [DIFFERENT_TERM]",search_suggestion:"Nenhum resultado encontrado para [SEARCH_TERM]. Tente uma das seguintes pesquisas:",searching:"Pesquisando por [SEARCH_TERM]..."},pi={thanks_to:fi,comments:di,direction:hi,strings:mi};var Zt={};y(Zt,{comments:()=>Ei,default:()=>Ti,direction:()=>Ri,strings:()=>bi,thanks_to:()=>gi});var gi="Bogdan Mateescu <bogdan@surfverse.com>",Ei="",Ri="ltr",bi={placeholder:"C\u0103utare",clear_search:"\u015Eterge\u0163i",load_more:"\xCEnc\u0103rca\u021Bi mai multe rezultate",search_label:"C\u0103uta\u021Bi \xEEn acest site",filters_label:"Filtre",zero_results:"Niciun rezultat pentru [SEARCH_TERM]",many_results:"[COUNT] rezultate pentru [SEARCH_TERM]",one_result:"[COUNT] rezultat pentru [SEARCH_TERM]",alt_search:"Niciun rezultat pentru [SEARCH_TERM]. 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Prueba una de las siguientes b\xFAsquedas:",searching:"Buscando [SEARCH_TERM]..."},Pr={thanks_to:zr,comments:Ur,direction:Dr,strings:Ir};var Nt={};y(Nt,{comments:()=>qr,default:()=>Wr,direction:()=>Br,strings:()=>Vr,thanks_to:()=>Lr});var Lr="Ali Khaleqi Yekta <https://yekta.dev>",qr="",Br="rtl",Vr={placeholder:"\u062C\u0633\u062A\u062C\u0648",clear_search:"\u067E\u0627\u06A9\u0633\u0627\u0632\u06CC",load_more:"\u0628\u0627\u0631\u06AF\u0630\u0627\u0631\u06CC \u0646\u062A\u0627\u06CC\u062C \u0628\u06CC\u0634\u062A\u0631",search_label:"\u062C\u0633\u062A\u062C\u0648 \u062F\u0631 \u0633\u0627\u06CC\u062A",filters_label:"\u0641\u06CC\u0644\u062A\u0631\u0647\u0627",zero_results:"\u0646\u062A\u06CC\u062C\u0647\u200C\u0627\u06CC \u0628\u0631\u0627\u06CC [SEARCH_TERM] \u06CC\u0627\u0641\u062A \u0646\u0634\u062F",many_results:"[COUNT] \u0646\u062A\u06CC\u062C\u0647 \u0628\u0631\u0627\u06CC [SEARCH_TERM] \u06CC\u0627\u0641\u062A \u0634\u062F",one_result:"[COUNT] \u0646\u062A\u06CC\u062C\u0647 \u0628\u0631\u0627\u06CC [SEARCH_TERM] \u06CC\u0627\u0641\u062A \u0634\u062F",alt_search:"\u0646\u062A\u06CC\u062C\u0647\u200C\u0627\u06CC \u0628\u0631\u0627\u06CC [SEARCH_TERM] \u06CC\u0627\u0641\u062A \u0646\u0634\u062F. \u062F\u0631 \u0639\u0648\u0636 \u0646\u062A\u0627\u06CC\u062C \u0628\u0631\u0627\u06CC [DIFFERENT_TERM] \u0646\u0645\u0627\u06CC\u0634 \u062F\u0627\u062F\u0647 \u0645\u06CC\u200C\u0634\u0648\u062F",search_suggestion:"\u0646\u062A\u06CC\u062C\u0647\u200C\u0627\u06CC \u0628\u0631\u0627\u06CC [SEARCH_TERM] \u06CC\u0627\u0641\u062A \u0646\u0634\u062F. \u06CC\u06A9\u06CC \u0627\u0632 \u062C\u0633\u062A\u062C\u0648\u0647\u0627\u06CC \u0632\u06CC\u0631 \u0631\u0627 \u0627\u0645\u062A\u062D\u0627\u0646 \u06A9\u0646\u06CC\u062F:",searching:"\u062F\u0631 \u062D\u0627\u0644 \u062C\u0633\u062A\u062C\u0648\u06CC [SEARCH_TERM]..."},Wr={thanks_to:Lr,comments:qr,direction:Br,strings:Vr};var Ot={};y(Ot,{comments:()=>Kr,default:()=>Zr,direction:()=>Jr,strings:()=>Yr,thanks_to:()=>Gr});var Gr="Valtteri Laitinen <dev@valtlai.fi>",Kr="",Jr="ltr",Yr={placeholder:"Haku",clear_search:"Tyhjenn\xE4",load_more:"Lataa lis\xE4\xE4 tuloksia",search_label:"Hae t\xE4lt\xE4 sivustolta",filters_label:"Suodattimet",zero_results:"Ei tuloksia haulle [SEARCH_TERM]",many_results:"[COUNT] tulosta haulle [SEARCH_TERM]",one_result:"[COUNT] tulos haulle [SEARCH_TERM]",alt_search:"Ei tuloksia haulle [SEARCH_TERM]. N\xE4ytet\xE4\xE4n tulokset sen sijaan haulle [DIFFERENT_TERM]",search_suggestion:"Ei tuloksia haulle [SEARCH_TERM]. Kokeile jotain seuraavista:",searching:"Haetaan [SEARCH_TERM]..."},Zr={thanks_to:Gr,comments:Kr,direction:Jr,strings:Yr};var jt={};y(jt,{comments:()=>Qr,default:()=>el,direction:()=>xr,strings:()=>$r,thanks_to:()=>Xr});var Xr="Nicolas Friedli <nicolas@theologique.ch>",Qr="",xr="ltr",$r={placeholder:"Rechercher",clear_search:"Nettoyer",load_more:"Charger plus de r\xE9sultats",search_label:"Recherche sur ce site",filters_label:"Filtres",zero_results:"Pas de r\xE9sultat pour [SEARCH_TERM]",many_results:"[COUNT] r\xE9sultats pour [SEARCH_TERM]",one_result:"[COUNT] r\xE9sultat pour [SEARCH_TERM]",alt_search:"Pas de r\xE9sultat pour [SEARCH_TERM]. Montre les r\xE9sultats pour [DIFFERENT_TERM] \xE0 la place",search_suggestion:"Pas de r\xE9sultat pour [SEARCH_TERM]. Essayer une des recherches suivantes:",searching:"Recherche [SEARCH_TERM]..."},el={thanks_to:Xr,comments:Qr,direction:xr,strings:$r};var zt={};y(zt,{comments:()=>nl,default:()=>ll,direction:()=>sl,strings:()=>rl,thanks_to:()=>tl});var tl="Pablo Villaverde <https://github.com/pvillaverde>",nl="",sl="ltr",rl={placeholder:"Buscar",clear_search:"Limpar",load_more:"Ver m\xE1is resultados",search_label:"Buscar neste sitio",filters_label:"Filtros",zero_results:"Non se atoparon resultados para [SEARCH_TERM]",many_results:"[COUNT] resultados atopados para [SEARCH_TERM]",one_result:"[COUNT] resultado atopado para [SEARCH_TERM]",alt_search:"Non se atoparon resultados para [SEARCH_TERM]. Amosando no seu lugar resultados para [DIFFERENT_TERM]",search_suggestion:"Non se atoparon resultados para [SEARCH_TERM]. Probe unha das seguintes pesquisas:",searching:"Buscando [SEARCH_TERM]..."},ll={thanks_to:tl,comments:nl,direction:sl,strings:rl};var Ut={};y(Ut,{comments:()=>al,default:()=>cl,direction:()=>ol,strings:()=>ul,thanks_to:()=>il});var il="Nir Tamir <nirtamir2@gmail.com>",al="",ol="rtl",ul={placeholder:"\u05D7\u05D9\u05E4\u05D5\u05E9",clear_search:"\u05E0\u05D9\u05E7\u05D5\u05D9",load_more:"\u05E2\u05D5\u05D3 \u05EA\u05D5\u05E6\u05D0\u05D5\u05EA",search_label:"\u05D7\u05D9\u05E4\u05D5\u05E9 \u05D1\u05D0\u05EA\u05E8 \u05D6\u05D4",filters_label:"\u05DE\u05E1\u05E0\u05E0\u05D9\u05DD",zero_results:"\u05DC\u05D0 \u05E0\u05DE\u05E6\u05D0\u05D5 \u05EA\u05D5\u05E6\u05D0\u05D5\u05EA \u05E2\u05D1\u05D5\u05E8 [SEARCH_TERM]",many_results:"\u05E0\u05DE\u05E6\u05D0\u05D5 [COUNT] \u05EA\u05D5\u05E6\u05D0\u05D5\u05EA \u05E2\u05D1\u05D5\u05E8 [SEARCH_TERM]",one_result:"\u05E0\u05DE\u05E6\u05D0\u05D4 \u05EA\u05D5\u05E6\u05D0\u05D4 \u05D0\u05D7\u05EA \u05E2\u05D1\u05D5\u05E8 [SEARCH_TERM]",alt_search:"\u05DC\u05D0 \u05E0\u05DE\u05E6\u05D0\u05D5 \u05EA\u05D5\u05E6\u05D0\u05D5\u05EA \u05E2\u05D1\u05D5\u05E8 [SEARCH_TERM]. \u05DE\u05D5\u05E6\u05D2\u05D5\u05EA \u05EA\u05D5\u05E6\u05D0\u05D5\u05EA \u05E2\u05D1\u05D5\u05E8 [DIFFERENT_TERM]",search_suggestion:"\u05DC\u05D0 \u05E0\u05DE\u05E6\u05D0\u05D5 \u05EA\u05D5\u05E6\u05D0\u05D5\u05EA \u05E2\u05D1\u05D5\u05E8 [SEARCH_TERM]. \u05E0\u05E1\u05D5 \u05D0\u05D7\u05D3 \u05DE\u05D4\u05D7\u05D9\u05E4\u05D5\u05E9\u05D9\u05DD \u05D4\u05D1\u05D0\u05D9\u05DD:",searching:"\u05DE\u05D7\u05E4\u05E9 \u05D0\u05EA [SEARCH_TERM]..."},cl={thanks_to:il,comments:al,direction:ol,strings:ul};var Dt={};y(Dt,{comments:()=>fl,default:()=>ml,direction:()=>dl,strings:()=>hl,thanks_to:()=>_l});var _l="Amit Yadav <amit@thetechbasket.com>",fl="",dl="ltr",hl={placeholder:"\u0916\u094B\u091C\u0947\u0902",clear_search:"\u0938\u093E\u092B \u0915\u0930\u0947\u0902",load_more:"\u0914\u0930 \u0905\u0927\u093F\u0915 \u092A\u0930\u093F\u0923\u093E\u092E \u0932\u094B\u0921 \u0915\u0930\u0947\u0902",search_label:"\u0907\u0938 \u0938\u093E\u0907\u091F \u092E\u0947\u0902 \u0916\u094B\u091C\u0947\u0902",filters_label:"\u092B\u093C\u093F\u0932\u094D\u091F\u0930",zero_results:"\u0915\u094B\u0908 \u092A\u0930\u093F\u0923\u093E\u092E [SEARCH_TERM] \u0915\u0947 \u0932\u093F\u090F \u0928\u0939\u0940\u0902 \u092E\u093F\u0932\u093E",many_results:"[COUNT] \u092A\u0930\u093F\u0923\u093E\u092E [SEARCH_TERM] \u0915\u0947 \u0932\u093F\u090F \u092E\u093F\u0932\u0947",one_result:"[COUNT] \u092A\u0930\u093F\u0923\u093E\u092E [SEARCH_TERM] \u0915\u0947 \u0932\u093F\u090F \u092E\u093F\u0932\u093E",alt_search:"[SEARCH_TERM] \u0915\u0947 \u0932\u093F\u090F \u0915\u094B\u0908 \u092A\u0930\u093F\u0923\u093E\u092E \u0928\u0939\u0940\u0902 \u092E\u093F\u0932\u093E\u0964 \u0907\u0938\u0915\u0947 \u092C\u091C\u093E\u092F [DIFFERENT_TERM] \u0915\u0947 \u0932\u093F\u090F \u092A\u0930\u093F\u0923\u093E\u092E \u0926\u093F\u0916\u093E \u0930\u0939\u093E \u0939\u0948",search_suggestion:"[SEARCH_TERM] \u0915\u0947 \u0932\u093F\u090F \u0915\u094B\u0908 \u092A\u0930\u093F\u0923\u093E\u092E \u0928\u0939\u0940\u0902 \u092E\u093F\u0932\u093E\u0964 \u0928\u093F\u092E\u094D\u0928\u0932\u093F\u0916\u093F\u0924 \u0916\u094B\u091C\u094B\u0902 \u092E\u0947\u0902 \u0938\u0947 \u0915\u094B\u0908 \u090F\u0915 \u0906\u091C\u093C\u092E\u093E\u090F\u0902:",searching:"[SEARCH_TERM] \u0915\u0940 \u0916\u094B\u091C \u0915\u0940 \u091C\u093E \u0930\u0939\u0940 \u0939\u0948..."},ml={thanks_to:_l,comments:fl,direction:dl,strings:hl};var It={};y(It,{comments:()=>gl,default:()=>bl,direction:()=>El,strings:()=>Rl,thanks_to:()=>pl});var pl="Diomed <https://github.com/diomed>",gl="",El="ltr",Rl={placeholder:"Tra\u017Ei",clear_search:"O\u010Disti",load_more:"U\u010Ditaj vi\u0161e rezultata",search_label:"Pretra\u017Ei ovu stranicu",filters_label:"Filteri",zero_results:"Nema rezultata za [SEARCH_TERM]",many_results:"[COUNT] rezultata za [SEARCH_TERM]",one_result:"[COUNT] rezultat za [SEARCH_TERM]",alt_search:"Nema rezultata za [SEARCH_TERM]. Prikazujem rezultate za [DIFFERENT_TERM]",search_suggestion:"Nema rezultata za [SEARCH_TERM]. Poku\u0161aj s jednom od ovih pretraga:",searching:"Pretra\u017Eujem [SEARCH_TERM]..."},bl={thanks_to:pl,comments:gl,direction:El,strings:Rl};var Pt={};y(Pt,{comments:()=>Cl,default:()=>yl,direction:()=>kl,strings:()=>Sl,thanks_to:()=>Tl});var Tl="Adam Laki <info@adamlaki.com>",Cl="",kl="ltr",Sl={placeholder:"Keres\xE9s",clear_search:"T\xF6rl\xE9s",load_more:"Tov\xE1bbi tal\xE1latok bet\xF6lt\xE9se",search_label:"Keres\xE9s az oldalon",filters_label:"Sz\u0171r\xE9s",zero_results:"Nincs tal\xE1lat a(z) [SEARCH_TERM] kifejez\xE9sre",many_results:"[COUNT] db tal\xE1lat a(z) [SEARCH_TERM] kifejez\xE9sre",one_result:"[COUNT] db tal\xE1lat a(z) [SEARCH_TERM] kifejez\xE9sre",alt_search:"Nincs tal\xE1lat a(z) [SEARCH_TERM] kifejez\xE9sre. Tal\xE1latok mutat\xE1sa ink\xE1bb a(z) [DIFFERENT_TERM] kifejez\xE9sre",search_suggestion:"Nincs tal\xE1lat a(z) [SEARCH_TERM] kifejez\xE9sre. Pr\xF3b\xE1ld meg a k\xF6vetkez\u0151 keres\xE9sek egyik\xE9t:",searching:"Keres\xE9s a(z) [SEARCH_TERM] kifejez\xE9sre..."},yl={thanks_to:Tl,comments:Cl,direction:kl,strings:Sl};var Lt={};y(Lt,{comments:()=>Al,default:()=>Hl,direction:()=>vl,strings:()=>wl,thanks_to:()=>Ml});var Ml="Nixentric",Al="",vl="ltr",wl={placeholder:"Cari",clear_search:"Bersihkan",load_more:"Muat lebih banyak hasil",search_label:"Telusuri situs ini",filters_label:"Filter",zero_results:"[SEARCH_TERM] tidak ditemukan",many_results:"Ditemukan [COUNT] hasil untuk [SEARCH_TERM]",one_result:"Ditemukan [COUNT] hasil untuk [SEARCH_TERM]",alt_search:"[SEARCH_TERM] tidak ditemukan. Menampilkan hasil [DIFFERENT_TERM] sebagai gantinya",search_suggestion:"[SEARCH_TERM] tidak ditemukan. Coba salah satu pencarian berikut ini:",searching:"Mencari [SEARCH_TERM]..."},Hl={thanks_to:Ml,comments:Al,direction:vl,strings:wl};var qt={};y(qt,{comments:()=>Nl,default:()=>zl,direction:()=>Ol,strings:()=>jl,thanks_to:()=>Fl});var Fl="Cosette Bruhns Alonso, Andrew Janco <apjanco@upenn.edu>",Nl="",Ol="ltr",jl={placeholder:"Cerca",clear_search:"Cancella la cronologia",load_more:"Mostra pi\xF9 risultati",search_label:"Cerca nel sito",filters_label:"Filtri di ricerca",zero_results:"Nessun risultato per [SEARCH_TERM]",many_results:"[COUNT] risultati per [SEARCH_TERM]",one_result:"[COUNT] risultato per [SEARCH_TERM]",alt_search:"Nessun risultato per [SEARCH_TERM]. Mostrando risultati per [DIFFERENT_TERM] come alternativa.",search_suggestion:"Nessun risultato per [SEARCH_TERM]. Prova una delle seguenti ricerche:",searching:"Cercando [SEARCH_TERM]..."},zl={thanks_to:Fl,comments:Nl,direction:Ol,strings:jl};var Bt={};y(Bt,{comments:()=>Dl,default:()=>Ll,direction:()=>Il,strings:()=>Pl,thanks_to:()=>Ul});var Ul="Tate",Dl="",Il="ltr",Pl={placeholder:"\u691C\u7D22",clear_search:"\u30AF\u30EA\u30A2",load_more:"\u6B21\u3092\u8AAD\u307F\u8FBC\u3080",search_label:"\u3053\u306E\u30B5\u30A4\u30C8\u3092\u691C\u7D22",filters_label:"\u30D5\u30A3\u30EB\u30BF",zero_results:"[SEARCH_TERM]\u306E\u691C\u7D22\u306B\u4E00\u81F4\u3059\u308B\u60C5\u5831\u306F\u3042\u308A\u307E\u305B\u3093\u3067\u3057\u305F",many_results:"[SEARCH_TERM]\u306E[COUNT]\u4EF6\u306E\u691C\u7D22\u7D50\u679C",one_result:"[SEARCH_TERM]\u306E[COUNT]\u4EF6\u306E\u691C\u7D22\u7D50\u679C",alt_search:"[SEARCH_TERM]\u306E\u691C\u7D22\u306B\u4E00\u81F4\u3059\u308B\u60C5\u5831\u306F\u3042\u308A\u307E\u305B\u3093\u3067\u3057\u305F\u3002[DIFFERENT_TERM]\u306E\u691C\u7D22\u7D50\u679C\u3092\u8868\u793A\u3057\u3066\u3044\u307E\u3059",search_suggestion:"[SEARCH_TERM]\u306E\u691C\u7D22\u306B\u4E00\u81F4\u3059\u308B\u60C5\u5831\u306F\u3042\u308A\u307E\u305B\u3093\u3067\u3057\u305F\u3002\u6B21\u306E\u3044\u305A\u308C\u304B\u306E\u691C\u7D22\u3092\u8A66\u3057\u3066\u304F\u3060\u3055\u3044",searching:"[SEARCH_TERM]\u3092\u691C\u7D22\u3057\u3066\u3044\u307E\u3059"},Ll={thanks_to:Ul,comments:Dl,direction:Il,strings:Pl};var Vt={};y(Vt,{comments:()=>Bl,default:()=>Gl,direction:()=>Vl,strings:()=>Wl,thanks_to:()=>ql});var ql="Seokho Son <https://github.com/seokho-son>",Bl="",Vl="ltr",Wl={placeholder:"\uAC80\uC0C9\uC5B4",clear_search:"\uBE44\uC6B0\uAE30",load_more:"\uAC80\uC0C9 \uACB0\uACFC \uB354 \uBCF4\uAE30",search_label:"\uC0AC\uC774\uD2B8 \uAC80\uC0C9",filters_label:"\uD544\uD130",zero_results:"[SEARCH_TERM]\uC5D0 \uB300\uD55C \uACB0\uACFC \uC5C6\uC74C",many_results:"[SEARCH_TERM]\uC5D0 \uB300\uD55C \uACB0\uACFC [COUNT]\uAC74",one_result:"[SEARCH_TERM]\uC5D0 \uB300\uD55C \uACB0\uACFC [COUNT]\uAC74",alt_search:"[SEARCH_TERM]\uC5D0 \uB300\uD55C \uACB0\uACFC \uC5C6\uC74C. [DIFFERENT_TERM]\uC5D0 \uB300\uD55C \uACB0\uACFC",search_suggestion:"[SEARCH_TERM]\uC5D0 \uB300\uD55C \uACB0\uACFC \uC5C6\uC74C. \uCD94\uCC9C \uAC80\uC0C9\uC5B4: ",searching:"[SEARCH_TERM] \uAC80\uC0C9 \uC911..."},Gl={thanks_to:ql,comments:Bl,direction:Vl,strings:Wl};var Wt={};y(Wt,{comments:()=>Jl,default:()=>Xl,direction:()=>Yl,strings:()=>Zl,thanks_to:()=>Kl});var Kl="",Jl="",Yl="ltr",Zl={placeholder:"Rapu",clear_search:"Whakakore",load_more:"Whakauta \u0113tahi otinga k\u0113",search_label:"Rapu",filters_label:"T\u0101tari",zero_results:"Otinga kore ki [SEARCH_TERM]",many_results:"[COUNT] otinga ki [SEARCH_TERM]",one_result:"[COUNT] otinga ki [SEARCH_TERM]",alt_search:"Otinga kore ki [SEARCH_TERM]. Otinga k\u0113 ki [DIFFERENT_TERM]",search_suggestion:"Otinga kore ki [SEARCH_TERM]. whakam\u0101tau ki ng\u0101 mea atu:",searching:"Rapu ki [SEARCH_TERM]..."},Xl={thanks_to:Kl,comments:Jl,direction:Yl,strings:Zl};var Gt={};y(Gt,{comments:()=>xl,default:()=>ti,direction:()=>$l,strings:()=>ei,thanks_to:()=>Ql});var Ql="Paul van Brouwershaven",xl="",$l="ltr",ei={placeholder:"Zoeken",clear_search:"Reset",load_more:"Meer resultaten laden",search_label:"Doorzoek deze site",filters_label:"Filters",zero_results:"Geen resultaten voor [SEARCH_TERM]",many_results:"[COUNT] resultaten voor [SEARCH_TERM]",one_result:"[COUNT] resultaat voor [SEARCH_TERM]",alt_search:"Geen resultaten voor [SEARCH_TERM]. In plaats daarvan worden resultaten voor [DIFFERENT_TERM] weergegeven",search_suggestion:"Geen resultaten voor [SEARCH_TERM]. Probeer een van de volgende zoekopdrachten:",searching:"Zoeken naar [SEARCH_TERM]..."},ti={thanks_to:Ql,comments:xl,direction:$l,strings:ei};var Kt={};y(Kt,{comments:()=>si,default:()=>ii,direction:()=>ri,strings:()=>li,thanks_to:()=>ni});var ni="Christopher Wingate",si="",ri="ltr",li={placeholder:"S\xF8k",clear_search:"Fjern",load_more:"Last flere resultater",search_label:"S\xF8k p\xE5 denne siden",filters_label:"Filtre",zero_results:"Ingen resultater for [SEARCH_TERM]",many_results:"[COUNT] resultater for [SEARCH_TERM]",one_result:"[COUNT] resultat for [SEARCH_TERM]",alt_search:"Ingen resultater for [SEARCH_TERM]. Viser resultater for [DIFFERENT_TERM] i stedet",search_suggestion:"Ingen resultater for [SEARCH_TERM]. Pr\xF8v en av disse s\xF8keordene i stedet:",searching:"S\xF8ker etter [SEARCH_TERM]"},ii={thanks_to:ni,comments:si,direction:ri,strings:li};var Jt={};y(Jt,{comments:()=>oi,default:()=>_i,direction:()=>ui,strings:()=>ci,thanks_to:()=>ai});var ai="",oi="",ui="ltr",ci={placeholder:"Szukaj",clear_search:"Wyczy\u015B\u0107",load_more:"Za\u0142aduj wi\u0119cej",search_label:"Przeszukaj t\u0119 stron\u0119",filters_label:"Filtry",zero_results:"Brak wynik\xF3w dla [SEARCH_TERM]",many_results:"[COUNT] wynik\xF3w dla [SEARCH_TERM]",one_result:"[COUNT] wynik dla [SEARCH_TERM]",alt_search:"Brak wynik\xF3w dla [SEARCH_TERM]. Wy\u015Bwietlam wyniki dla [DIFFERENT_TERM]",search_suggestion:"Brak wynik\xF3w dla [SEARCH_TERM]. Pokrewne wyniki wyszukiwania:",searching:"Szukam [SEARCH_TERM]..."},_i={thanks_to:ai,comments:oi,direction:ui,strings:ci};var Yt={};y(Yt,{comments:()=>di,default:()=>pi,direction:()=>hi,strings:()=>mi,thanks_to:()=>fi});var fi="Jonatah",di="",hi="ltr",mi={placeholder:"Pesquisar",clear_search:"Limpar",load_more:"Ver mais resultados",search_label:"Pesquisar",filters_label:"Filtros",zero_results:"Nenhum resultado encontrado para [SEARCH_TERM]",many_results:"[COUNT] resultados encontrados para [SEARCH_TERM]",one_result:"[COUNT] resultado encontrado para [SEARCH_TERM]",alt_search:"Nenhum resultado encontrado para [SEARCH_TERM]. Exibindo resultados para [DIFFERENT_TERM]",search_suggestion:"Nenhum resultado encontrado para [SEARCH_TERM]. 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index 8a4c4c75..00000000
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diff --git a/pagefind/pagefind.en_fe283df5ce.pf_meta b/pagefind/pagefind.en_fe283df5ce.pf_meta
new file mode 100644
index 00000000..e2ac7de1
Binary files /dev/null and b/pagefind/pagefind.en_fe283df5ce.pf_meta differ
diff --git a/pagefind/pagefind.js b/pagefind/pagefind.js
index 0ea99ad0..035a4386 100644
--- a/pagefind/pagefind.js
+++ b/pagefind/pagefind.js
@@ -1,4 +1,4 @@
-const pagefind_version="1.2.0";let wasm_bindgen;(function(){const __exports={};let script_src;if(typeof document!=='undefined'&&document.currentScript!==null){script_src=new URL("UNHANDLED",location.href).toString()}let wasm=undefined;let cachedUint8Memory0=null;function getUint8Memory0(){if(cachedUint8Memory0===null||cachedUint8Memory0.byteLength===0){cachedUint8Memory0=new Uint8Array(wasm.memory.buffer)}return cachedUint8Memory0}let WASM_VECTOR_LEN=0;function passArray8ToWasm0(arg,malloc){const ptr=malloc(arg.length*1,1)>>>0;getUint8Memory0().set(arg,ptr/1);WASM_VECTOR_LEN=arg.length;return ptr}__exports.init_pagefind=function(metadata_bytes){const ptr0=passArray8ToWasm0(metadata_bytes,wasm.__wbindgen_malloc);const len0=WASM_VECTOR_LEN;const ret=wasm.init_pagefind(ptr0,len0);return ret>>>0};const cachedTextEncoder=(typeof TextEncoder!=='undefined'?new TextEncoder('utf-8'):{encode:()=>{throw Error('TextEncoder not available')}});const encodeString=(typeof 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ptr0=passStringToWasm0(weights,wasm.__wbindgen_malloc,wasm.__wbindgen_realloc);const len0=WASM_VECTOR_LEN;const ret=wasm.set_ranking_weights(ptr,ptr0,len0);return ret>>>0};__exports.load_index_chunk=function(ptr,chunk_bytes){const ptr0=passArray8ToWasm0(chunk_bytes,wasm.__wbindgen_malloc);const len0=WASM_VECTOR_LEN;const ret=wasm.load_index_chunk(ptr,ptr0,len0);return ret>>>0};__exports.load_filter_chunk=function(ptr,chunk_bytes){const ptr0=passArray8ToWasm0(chunk_bytes,wasm.__wbindgen_malloc);const len0=WASM_VECTOR_LEN;const ret=wasm.load_filter_chunk(ptr,ptr0,len0);return ret>>>0};__exports.add_synthetic_filter=function(ptr,filter){const ptr0=passStringToWasm0(filter,wasm.__wbindgen_malloc,wasm.__wbindgen_realloc);const len0=WASM_VECTOR_LEN;const ret=wasm.add_synthetic_filter(ptr,ptr0,len0);return ret>>>0};let cachedInt32Memory0=null;function getInt32Memory0(){if(cachedInt32Memory0===null||cachedInt32Memory0.byteLength===0){cachedInt32Memory0=new Int32Array(wasm.memory.buffer)}return cachedInt32Memory0}const cachedTextDecoder=(typeof TextDecoder!=='undefined'?new TextDecoder('utf-8',{ignoreBOM:true,fatal:true}):{decode:()=>{throw Error('TextDecoder not available')}});if(typeof TextDecoder!=='undefined'){cachedTextDecoder.decode()};function getStringFromWasm0(ptr,len){ptr=ptr>>>0;return cachedTextDecoder.decode(getUint8Memory0().subarray(ptr,ptr+len))}__exports.request_indexes=function(ptr,query){let deferred2_0;let deferred2_1;try{const retptr=wasm.__wbindgen_add_to_stack_pointer(-16);const ptr0=passStringToWasm0(query,wasm.__wbindgen_malloc,wasm.__wbindgen_realloc);const len0=WASM_VECTOR_LEN;wasm.request_indexes(retptr,ptr,ptr0,len0);var r0=getInt32Memory0()[retptr/4+0];var r1=getInt32Memory0()[retptr/4+1];deferred2_0=r0;deferred2_1=r1;return getStringFromWasm0(r0,r1)}finally{wasm.__wbindgen_add_to_stack_pointer(16);wasm.__wbindgen_free(deferred2_0,deferred2_1,1)}};__exports.request_filter_indexes=function(ptr,filters){let deferred2_0;let deferred2_1;try{const retptr=wasm.__wbindgen_add_to_stack_pointer(-16);const ptr0=passStringToWasm0(filters,wasm.__wbindgen_malloc,wasm.__wbindgen_realloc);const len0=WASM_VECTOR_LEN;wasm.request_filter_indexes(retptr,ptr,ptr0,len0);var r0=getInt32Memory0()[retptr/4+0];var r1=getInt32Memory0()[retptr/4+1];deferred2_0=r0;deferred2_1=r1;return getStringFromWasm0(r0,r1)}finally{wasm.__wbindgen_add_to_stack_pointer(16);wasm.__wbindgen_free(deferred2_0,deferred2_1,1)}};__exports.request_all_filter_indexes=function(ptr){let deferred1_0;let deferred1_1;try{const retptr=wasm.__wbindgen_add_to_stack_pointer(-16);wasm.request_all_filter_indexes(retptr,ptr);var r0=getInt32Memory0()[retptr/4+0];var r1=getInt32Memory0()[retptr/4+1];deferred1_0=r0;deferred1_1=r1;return getStringFromWasm0(r0,r1)}finally{wasm.__wbindgen_add_to_stack_pointer(16);wasm.__wbindgen_free(deferred1_0,deferred1_1,1)}};__exports.filters=function(ptr){let deferred1_0;let deferred1_1;try{const retptr=wasm.__wbindgen_add_to_stack_pointer(-16);wasm.filters(retptr,ptr);var r0=getInt32Memory0()[retptr/4+0];var r1=getInt32Memory0()[retptr/4+1];deferred1_0=r0;deferred1_1=r1;return getStringFromWasm0(r0,r1)}finally{wasm.__wbindgen_add_to_stack_pointer(16);wasm.__wbindgen_free(deferred1_0,deferred1_1,1)}};__exports.search=function(ptr,query,filter,sort,exact){let deferred4_0;let deferred4_1;try{const retptr=wasm.__wbindgen_add_to_stack_pointer(-16);const ptr0=passStringToWasm0(query,wasm.__wbindgen_malloc,wasm.__wbindgen_realloc);const len0=WASM_VECTOR_LEN;const ptr1=passStringToWasm0(filter,wasm.__wbindgen_malloc,wasm.__wbindgen_realloc);const len1=WASM_VECTOR_LEN;const ptr2=passStringToWasm0(sort,wasm.__wbindgen_malloc,wasm.__wbindgen_realloc);const len2=WASM_VECTOR_LEN;wasm.search(retptr,ptr,ptr0,len0,ptr1,len1,ptr2,len2,exact);var r0=getInt32Memory0()[retptr/4+0];var r1=getInt32Memory0()[retptr/4+1];deferred4_0=r0;deferred4_1=r1;return getStringFromWasm0(r0,r1)}finally{wasm.__wbindgen_add_to_stack_pointer(16);wasm.__wbindgen_free(deferred4_0,deferred4_1,1)}};async function __wbg_load(module,imports){if(typeof Response==='function'&&module instanceof Response){if(typeof WebAssembly.instantiateStreaming==='function'){try{return await WebAssembly.instantiateStreaming(module,imports)}catch(e){if(module.headers.get('Content-Type')!='application/wasm'){console.warn("`WebAssembly.instantiateStreaming` failed because your server does not serve wasm with `application/wasm` MIME type. 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max=function(a){var m=a[0];for(var i2=1;i2<a.length;++i2){if(a[i2]>m)m=a[i2]}return m};var bits=function(d,p,m){var o=p/8|0;return(d[o]|d[o+1]<<8)>>(p&7)&m};var bits16=function(d,p){var o=p/8|0;return(d[o]|d[o+1]<<8|d[o+2]<<16)>>(p&7)};var shft=function(p){return(p+7)/8|0};var slc=function(v,s,e){if(s==null||s<0)s=0;if(e==null||e>v.length)e=v.length;var n=new(v.BYTES_PER_ELEMENT==2?u16:v.BYTES_PER_ELEMENT==4?u32:u8)(e-s);n.set(v.subarray(s,e));return n};var ec=["unexpected EOF","invalid block type","invalid length/literal","invalid distance","stream finished","no stream handler",,"no callback","invalid UTF-8 data","extra field too long","date not in range 1980-2099","filename too long","stream finishing","invalid zip data"];var err=function(ind,msg,nt){var e=new Error(msg||ec[ind]);e.code=ind;if(Error.captureStackTrace)Error.captureStackTrace(e,err);if(!nt)throw e;return e};var inflt=function(dat,buf,st){var sl=dat.length;if(!sl||st&&st.f&&!st.l)return buf||new u8(0);var noBuf=!buf||st;var noSt=!st||st.i;if(!st)st={};if(!buf)buf=new u8(sl*3);var cbuf=function(l2){var bl=buf.length;if(l2>bl){var nbuf=new u8(Math.max(bl*2,l2));nbuf.set(buf);buf=nbuf}};var final=st.f||0,pos=st.p||0,bt=st.b||0,lm=st.l,dm=st.d,lbt=st.m,dbt=st.n;var tbts=sl*8;do{if(!lm){final=bits(dat,pos,1);var type=bits(dat,pos+1,3);pos+=3;if(!type){var s=shft(pos)+4,l=dat[s-4]|dat[s-3]<<8,t=s+l;if(t>sl){if(noSt)err(0);break}if(noBuf)cbuf(bt+l);buf.set(dat.subarray(s,t),bt);st.b=bt+=l,st.p=pos=t*8,st.f=final;continue}else if(type==1)lm=flrm,dm=fdrm,lbt=9,dbt=5;else if(type==2){var hLit=bits(dat,pos,31)+257,hcLen=bits(dat,pos+10,15)+4;var tl=hLit+bits(dat,pos+5,31)+1;pos+=14;var ldt=new u8(tl);var clt=new u8(19);for(var i2=0;i2<hcLen;++i2){clt[clim[i2]]=bits(dat,pos+i2*3,7)}pos+=hcLen*3;var clb=max(clt),clbmsk=(1<<clb)-1;var clm=hMap(clt,clb,1);for(var i2=0;i2<tl;){var r=clm[bits(dat,pos,clbmsk)];pos+=r&15;var s=r>>>4;if(s<16){ldt[i2++]=s}else{var c=0,n=0;if(s==16)n=3+bits(dat,pos,3),pos+=2,c=ldt[i2-1];else if(s==17)n=3+bits(dat,pos,7),pos+=3;else if(s==18)n=11+bits(dat,pos,127),pos+=7;while(n--)ldt[i2++]=c}}var lt=ldt.subarray(0,hLit),dt=ldt.subarray(hLit);lbt=max(lt);dbt=max(dt);lm=hMap(lt,lbt,1);dm=hMap(dt,dbt,1)}else err(1);if(pos>tbts){if(noSt)err(0);break}}if(noBuf)cbuf(bt+131072);var lms=(1<<lbt)-1,dms=(1<<dbt)-1;var lpos=pos;for(;;lpos=pos){var c=lm[bits16(dat,pos)&lms],sym=c>>>4;pos+=c&15;if(pos>tbts){if(noSt)err(0);break}if(!c)err(2);if(sym<256)buf[bt++]=sym;else if(sym==256){lpos=pos,lm=null;break}else{var add=sym-254;if(sym>264){var i2=sym-257,b=fleb[i2];add=bits(dat,pos,(1<<b)-1)+fl[i2];pos+=b}var d=dm[bits16(dat,pos)&dms],dsym=d>>>4;if(!d)err(3);pos+=d&15;var dt=fd[dsym];if(dsym>3){var b=fdeb[dsym];dt+=bits16(dat,pos)&(1<<b)-1,pos+=b}if(pos>tbts){if(noSt)err(0);break}if(noBuf)cbuf(bt+131072);var end=bt+add;for(;bt<end;bt+=4){buf[bt]=buf[bt-dt];buf[bt+1]=buf[bt+1-dt];buf[bt+2]=buf[bt+2-dt];buf[bt+3]=buf[bt+3-dt]}bt=end}}st.l=lm,st.p=lpos,st.b=bt,st.f=final;if(lm)final=1,st.m=lbt,st.d=dm,st.n=dbt}while(!final);return bt==buf.length?buf:slc(buf,0,bt)};var et=new u8(0);var gzs=function(d){if(d[0]!=31||d[1]!=139||d[2]!=8)err(6,"invalid gzip data");var flg=d[3];var st=10;if(flg&4)st+=d[10]|(d[11]<<8)+2;for(var zs=(flg>>3&1)+(flg>>4&1);zs>0;zs-=!d[st++]);return st+(flg&2)};var gzl=function(d){var l=d.length;return(d[l-4]|d[l-3]<<8|d[l-2]<<16|d[l-1]<<24)>>>0};function gunzipSync(data,out){return inflt(data.subarray(gzs(data),-8),out||new u8(gzl(data)))}var td=typeof TextDecoder!="undefined"&&new TextDecoder();var tds=0;try{td.decode(et,{stream:true});tds=1}catch(e){}var gz_default=gunzipSync;var calculate_excerpt_region=(word_positions,excerpt_length)=>{if(word_positions.length===0){return 0}let words=[];for(const word of word_positions){words[word.location]=words[word.location]||0;words[word.location]+=word.balanced_score}if(words.length<=excerpt_length){return 0}let densest=words.slice(0,excerpt_length).reduce((partialSum,a)=>partialSum+a,0);let working_sum=densest;let densest_at=[0];for(let i2=0;i2<words.length;i2++){const boundary=i2+excerpt_length;working_sum+=(words[boundary]??0)-(words[i2]??0);if(working_sum>densest){densest=working_sum;densest_at=[i2]}else if(working_sum===densest&&densest_at[densest_at.length-1]===i2-1){densest_at.push(i2)}}let midpoint=densest_at[Math.floor(densest_at.length/2)];return midpoint};var build_excerpt=(content,start,length,locations,not_before,not_from)=>{let is_zws_delimited=content.includes("\u200B");let fragment_words=[];if(is_zws_delimited){fragment_words=content.split("\u200B")}else{fragment_words=content.split(/[\r\n\s]+/g)}for(let word of locations){if(fragment_words[word]?.startsWith(`<mark>`)){continue}fragment_words[word]=`<mark>${fragment_words[word]}</mark>`}let endcap=not_from??fragment_words.length;let startcap=not_before??0;if(endcap-startcap<length){length=endcap-startcap}if(start+length>endcap){start=endcap-length}if(start<startcap){start=startcap}return fragment_words.slice(start,start+length).join(is_zws_delimited?"":" ").trim()};var calculate_sub_results=(fragment,desired_excerpt_length)=>{const anchors=fragment.anchors.filter((a)=>/h\d/i.test(a.element)&&a.text?.length&&/\S/.test(a.text)).sort((a,b)=>a.location-b.location);const results=[];let current_anchor_position=0;let current_anchor={title:fragment.meta["title"],url:fragment.url,weighted_locations:[],locations:[],excerpt:""};const add_result=(end_range)=>{if(current_anchor.locations.length){const relative_weighted_locations=current_anchor.weighted_locations.map((l)=>{return{weight:l.weight,balanced_score:l.balanced_score,location:l.location-current_anchor_position}});const excerpt_start=calculate_excerpt_region(relative_weighted_locations,desired_excerpt_length)+current_anchor_position;const excerpt_length=end_range?Math.min(end_range-excerpt_start,desired_excerpt_length):desired_excerpt_length;current_anchor.excerpt=build_excerpt(fragment.raw_content??"",excerpt_start,excerpt_length,current_anchor.locations,current_anchor_position,end_range);results.push(current_anchor)}};for(let word of fragment.weighted_locations){if(!anchors.length||word.location<anchors[0].location){current_anchor.weighted_locations.push(word);current_anchor.locations.push(word.location)}else{let next_anchor=anchors.shift();add_result(next_anchor.location);while(anchors.length&&word.location>=anchors[0].location){next_anchor=anchors.shift()}let anchored_url=fragment.url;try{const url_is_fq=/^((https?:)?\/\/)/.test(anchored_url);if(url_is_fq){let fq_url=new URL(anchored_url);fq_url.hash=next_anchor.id;anchored_url=fq_url.toString()}else{if(!/^\//.test(anchored_url)){anchored_url=`/${anchored_url}`}let fq_url=new URL(`https://example.com${anchored_url}`);fq_url.hash=next_anchor.id;anchored_url=fq_url.toString().replace(/^https:\/\/example.com/,"")}}catch(e){console.error(`Pagefind: Couldn't process ${anchored_url} for a search result`)}current_anchor_position=next_anchor.location;current_anchor={title:next_anchor.text,url:anchored_url,anchor:next_anchor,weighted_locations:[word],locations:[word.location],excerpt:""}}}add_result(anchors[0]?.location);return results};var asyncSleep=async(ms=100)=>{return new Promise((r)=>setTimeout(r,ms))};var PagefindInstance=class{constructor(opts={}){this.version=pagefind_version;this.backend=wasm_bindgen;this.decoder=new TextDecoder("utf-8");this.wasm=null;this.basePath=opts.basePath||"/pagefind/";this.primary=opts.primary||false;if(this.primary&&!opts.basePath){this.initPrimary()}if(/[^\/]$/.test(this.basePath)){this.basePath=`${this.basePath}/`}if(window?.location?.origin&&this.basePath.startsWith(window.location.origin)){this.basePath=this.basePath.replace(window.location.origin,"")}this.baseUrl=opts.baseUrl||this.defaultBaseUrl();if(!/^(\/|https?:\/\/)/.test(this.baseUrl)){this.baseUrl=`/${this.baseUrl}`}this.indexWeight=opts.indexWeight??1;this.excerptLength=opts.excerptLength??30;this.mergeFilter=opts.mergeFilter??{};this.ranking=opts.ranking;this.highlightParam=opts.highlightParam??null;this.loaded_chunks={};this.loaded_filters={};this.loaded_fragments={};this.raw_ptr=null;this.searchMeta=null;this.languages=null}initPrimary(){let derivedBasePath=import.meta.url.match(/^(.*\/)pagefind.js.*$/)?.[1];if(derivedBasePath){this.basePath=derivedBasePath}else{console.warn(["Pagefind couldn't determine the base of the bundle from the import path. Falling back to the default.","Set a basePath option when initialising Pagefind to ignore this message."].join("\n"))}}defaultBaseUrl(){let default_base=this.basePath.match(/^(.*\/)_?pagefind/)?.[1];return default_base||"/"}async options(options2){const opts=["basePath","baseUrl","indexWeight","excerptLength","mergeFilter","highlightParam","ranking"];for(const[k,v]of Object.entries(options2)){if(k==="mergeFilter"){let filters2=this.stringifyFilters(v);let ptr=await this.getPtr();this.raw_ptr=this.backend.add_synthetic_filter(ptr,filters2)}else if(k==="ranking"){await this.set_ranking(options2.ranking)}else if(opts.includes(k)){if(k==="basePath"&&typeof v==="string")this.basePath=v;if(k==="baseUrl"&&typeof v==="string")this.baseUrl=v;if(k==="indexWeight"&&typeof v==="number")this.indexWeight=v;if(k==="excerptLength"&&typeof v==="number")this.excerptLength=v;if(k==="mergeFilter"&&typeof v==="object")this.mergeFilter=v;if(k==="highlightParam"&&typeof v==="string")this.highlightParam=v}else{console.warn(`Unknown Pagefind option ${k}. Allowed options: [${opts.join(", ")}]`)}}}decompress(data,file="unknown file"){if(this.decoder.decode(data.slice(0,12))==="pagefind_dcd"){return data.slice(12)}data=gz_default(data);if(this.decoder.decode(data.slice(0,12))!=="pagefind_dcd"){console.error(`Decompressing ${file} appears to have failed: Missing signature`);return data}return data.slice(12)}async set_ranking(ranking){if(!ranking)return;let rankingWeights={term_similarity:ranking.termSimilarity??null,page_length:ranking.pageLength??null,term_saturation:ranking.termSaturation??null,term_frequency:ranking.termFrequency??null};let ptr=await this.getPtr();this.raw_ptr=this.backend.set_ranking_weights(ptr,JSON.stringify(rankingWeights))}async init(language,opts){await this.loadEntry();let index=this.findIndex(language);let lang_wasm=index.wasm?index.wasm:"unknown";let resources=[this.loadMeta(index.hash)];if(opts.load_wasm===true){resources.push(this.loadWasm(lang_wasm))}await Promise.all(resources);this.raw_ptr=this.backend.init_pagefind(new Uint8Array(this.searchMeta));if(Object.keys(this.mergeFilter)?.length){let filters2=this.stringifyFilters(this.mergeFilter);let ptr=await this.getPtr();this.raw_ptr=this.backend.add_synthetic_filter(ptr,filters2)}if(this.ranking){await this.set_ranking(this.ranking)}}async loadEntry(){try{let entry_response=await fetch(`${this.basePath}pagefind-entry.json?ts=${Date.now()}`);let entry_json=await entry_response.json();this.languages=entry_json.languages;if(entry_json.version!==this.version){if(this.primary){console.warn(["Pagefind JS version doesn't match the version in your search index.",`Pagefind JS: ${this.version}. Pagefind index: ${entry_json.version}`,"If you upgraded Pagefind recently, you likely have a cached pagefind.js file.","If you encounter any search errors, try clearing your cache."].join("\n"))}else{console.warn(["Merging a Pagefind index from a different version than the main Pagefind instance.",`Main Pagefind JS: ${this.version}. Merged index (${this.basePath}): ${entry_json.version}`,"If you encounter any search errors, make sure that both sites are running the same version of Pagefind."].join("\n"))}}}catch(e){console.error(`Failed to load Pagefind metadata:
+const pagefind_version="1.3.0";let wasm_bindgen;(function(){const __exports={};let script_src;if(typeof document!=='undefined'&&document.currentScript!==null){script_src=new URL("UNHANDLED",location.href).toString()}let wasm=undefined;let cachedUint8Memory0=null;function getUint8Memory0(){if(cachedUint8Memory0===null||cachedUint8Memory0.byteLength===0){cachedUint8Memory0=new Uint8Array(wasm.memory.buffer)}return cachedUint8Memory0}let WASM_VECTOR_LEN=0;function passArray8ToWasm0(arg,malloc){const ptr=malloc(arg.length*1,1)>>>0;getUint8Memory0().set(arg,ptr/1);WASM_VECTOR_LEN=arg.length;return ptr}__exports.init_pagefind=function(metadata_bytes){const ptr0=passArray8ToWasm0(metadata_bytes,wasm.__wbindgen_malloc);const len0=WASM_VECTOR_LEN;const ret=wasm.init_pagefind(ptr0,len0);return ret>>>0};const cachedTextEncoder=(typeof TextEncoder!=='undefined'?new TextEncoder('utf-8'):{encode:()=>{throw Error('TextEncoder not available')}});const encodeString=(typeof cachedTextEncoder.encodeInto==='function'?function(arg,view){return cachedTextEncoder.encodeInto(arg,view)}:function(arg,view){const buf=cachedTextEncoder.encode(arg);view.set(buf);return{read:arg.length,written:buf.length}});function passStringToWasm0(arg,malloc,realloc){if(realloc===undefined){const buf=cachedTextEncoder.encode(arg);const ptr=malloc(buf.length,1)>>>0;getUint8Memory0().subarray(ptr,ptr+buf.length).set(buf);WASM_VECTOR_LEN=buf.length;return ptr}let len=arg.length;let ptr=malloc(len,1)>>>0;const mem=getUint8Memory0();let offset=0;for(;offset<len;offset++){const code=arg.charCodeAt(offset);if(code>0x7F)break;mem[ptr+offset]=code}if(offset!==len){if(offset!==0){arg=arg.slice(offset)}ptr=realloc(ptr,len,len=offset+arg.length*3,1)>>>0;const view=getUint8Memory0().subarray(ptr+offset,ptr+len);const ret=encodeString(arg,view);offset+=ret.written;ptr=realloc(ptr,len,offset,1)>>>0}WASM_VECTOR_LEN=offset;return ptr}__exports.set_ranking_weights=function(ptr,weights){const ptr0=passStringToWasm0(weights,wasm.__wbindgen_malloc,wasm.__wbindgen_realloc);const len0=WASM_VECTOR_LEN;const ret=wasm.set_ranking_weights(ptr,ptr0,len0);return ret>>>0};__exports.load_index_chunk=function(ptr,chunk_bytes){const ptr0=passArray8ToWasm0(chunk_bytes,wasm.__wbindgen_malloc);const len0=WASM_VECTOR_LEN;const ret=wasm.load_index_chunk(ptr,ptr0,len0);return ret>>>0};__exports.load_filter_chunk=function(ptr,chunk_bytes){const ptr0=passArray8ToWasm0(chunk_bytes,wasm.__wbindgen_malloc);const len0=WASM_VECTOR_LEN;const ret=wasm.load_filter_chunk(ptr,ptr0,len0);return ret>>>0};__exports.add_synthetic_filter=function(ptr,filter){const ptr0=passStringToWasm0(filter,wasm.__wbindgen_malloc,wasm.__wbindgen_realloc);const len0=WASM_VECTOR_LEN;const ret=wasm.add_synthetic_filter(ptr,ptr0,len0);return ret>>>0};let cachedInt32Memory0=null;function getInt32Memory0(){if(cachedInt32Memory0===null||cachedInt32Memory0.byteLength===0){cachedInt32Memory0=new Int32Array(wasm.memory.buffer)}return cachedInt32Memory0}const cachedTextDecoder=(typeof TextDecoder!=='undefined'?new TextDecoder('utf-8',{ignoreBOM:true,fatal:true}):{decode:()=>{throw Error('TextDecoder not available')}});if(typeof TextDecoder!=='undefined'){cachedTextDecoder.decode()};function getStringFromWasm0(ptr,len){ptr=ptr>>>0;return cachedTextDecoder.decode(getUint8Memory0().subarray(ptr,ptr+len))}__exports.request_indexes=function(ptr,query){let deferred2_0;let deferred2_1;try{const retptr=wasm.__wbindgen_add_to_stack_pointer(-16);const ptr0=passStringToWasm0(query,wasm.__wbindgen_malloc,wasm.__wbindgen_realloc);const len0=WASM_VECTOR_LEN;wasm.request_indexes(retptr,ptr,ptr0,len0);var r0=getInt32Memory0()[retptr/4+0];var r1=getInt32Memory0()[retptr/4+1];deferred2_0=r0;deferred2_1=r1;return getStringFromWasm0(r0,r1)}finally{wasm.__wbindgen_add_to_stack_pointer(16);wasm.__wbindgen_free(deferred2_0,deferred2_1,1)}};__exports.request_filter_indexes=function(ptr,filters){let deferred2_0;let deferred2_1;try{const retptr=wasm.__wbindgen_add_to_stack_pointer(-16);const ptr0=passStringToWasm0(filters,wasm.__wbindgen_malloc,wasm.__wbindgen_realloc);const len0=WASM_VECTOR_LEN;wasm.request_filter_indexes(retptr,ptr,ptr0,len0);var r0=getInt32Memory0()[retptr/4+0];var r1=getInt32Memory0()[retptr/4+1];deferred2_0=r0;deferred2_1=r1;return getStringFromWasm0(r0,r1)}finally{wasm.__wbindgen_add_to_stack_pointer(16);wasm.__wbindgen_free(deferred2_0,deferred2_1,1)}};__exports.request_all_filter_indexes=function(ptr){let deferred1_0;let deferred1_1;try{const retptr=wasm.__wbindgen_add_to_stack_pointer(-16);wasm.request_all_filter_indexes(retptr,ptr);var r0=getInt32Memory0()[retptr/4+0];var r1=getInt32Memory0()[retptr/4+1];deferred1_0=r0;deferred1_1=r1;return getStringFromWasm0(r0,r1)}finally{wasm.__wbindgen_add_to_stack_pointer(16);wasm.__wbindgen_free(deferred1_0,deferred1_1,1)}};__exports.filters=function(ptr){let deferred1_0;let deferred1_1;try{const retptr=wasm.__wbindgen_add_to_stack_pointer(-16);wasm.filters(retptr,ptr);var r0=getInt32Memory0()[retptr/4+0];var r1=getInt32Memory0()[retptr/4+1];deferred1_0=r0;deferred1_1=r1;return getStringFromWasm0(r0,r1)}finally{wasm.__wbindgen_add_to_stack_pointer(16);wasm.__wbindgen_free(deferred1_0,deferred1_1,1)}};__exports.search=function(ptr,query,filter,sort,exact){let deferred4_0;let deferred4_1;try{const retptr=wasm.__wbindgen_add_to_stack_pointer(-16);const ptr0=passStringToWasm0(query,wasm.__wbindgen_malloc,wasm.__wbindgen_realloc);const len0=WASM_VECTOR_LEN;const ptr1=passStringToWasm0(filter,wasm.__wbindgen_malloc,wasm.__wbindgen_realloc);const len1=WASM_VECTOR_LEN;const ptr2=passStringToWasm0(sort,wasm.__wbindgen_malloc,wasm.__wbindgen_realloc);const len2=WASM_VECTOR_LEN;wasm.search(retptr,ptr,ptr0,len0,ptr1,len1,ptr2,len2,exact);var r0=getInt32Memory0()[retptr/4+0];var r1=getInt32Memory0()[retptr/4+1];deferred4_0=r0;deferred4_1=r1;return getStringFromWasm0(r0,r1)}finally{wasm.__wbindgen_add_to_stack_pointer(16);wasm.__wbindgen_free(deferred4_0,deferred4_1,1)}};async function __wbg_load(module,imports){if(typeof Response==='function'&&module instanceof Response){if(typeof WebAssembly.instantiateStreaming==='function'){try{return await WebAssembly.instantiateStreaming(module,imports)}catch(e){if(module.headers.get('Content-Type')!='application/wasm'){console.warn("`WebAssembly.instantiateStreaming` failed because your server does not serve wasm with `application/wasm` MIME type. Falling back to `WebAssembly.instantiate` which is slower. Original error:\n",e)}else{throw e}}}const bytes=await module.arrayBuffer();return await WebAssembly.instantiate(bytes,imports)}else{const instance=await WebAssembly.instantiate(module,imports);if(instance instanceof WebAssembly.Instance){return{instance,module}}else{return instance}}}function __wbg_get_imports(){const imports={};imports.wbg={};return imports}function __wbg_init_memory(imports,maybe_memory){}function __wbg_finalize_init(instance,module){wasm=instance.exports;__wbg_init.__wbindgen_wasm_module=module;cachedInt32Memory0=null;cachedUint8Memory0=null;return wasm}function initSync(module){if(wasm!==undefined)return wasm;const imports=__wbg_get_imports();__wbg_init_memory(imports);if(!(module instanceof WebAssembly.Module)){module=new WebAssembly.Module(module)}const instance=new WebAssembly.Instance(module,imports);return __wbg_finalize_init(instance,module)}async function __wbg_init(input){if(wasm!==undefined)return wasm;if(typeof input==='undefined'&&typeof script_src!=='undefined'){input=script_src.replace(/\.js$/,'_bg.wasm')}const imports=__wbg_get_imports();if(typeof input==='string'||(typeof Request==='function'&&input instanceof Request)||(typeof URL==='function'&&input instanceof URL)){input=fetch(input)}__wbg_init_memory(imports);const{instance,module}=await __wbg_load(await input,imports);return __wbg_finalize_init(instance,module)}wasm_bindgen=Object.assign(__wbg_init,{initSync},__exports)})();var u8=Uint8Array;var u16=Uint16Array;var u32=Uint32Array;var fleb=new u8([0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,0,0,0,0]);var fdeb=new u8([0,0,0,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,0,0]);var clim=new u8([16,17,18,0,8,7,9,6,10,5,11,4,12,3,13,2,14,1,15]);var freb=function(eb,start){var b=new u16(31);for(var i2=0;i2<31;++i2){b[i2]=start+=1<<eb[i2-1]}var r=new u32(b[30]);for(var i2=1;i2<30;++i2){for(var j=b[i2];j<b[i2+1];++j){r[j]=j-b[i2]<<5|i2}}return[b,r]};var _a=freb(fleb,2);var fl=_a[0];var revfl=_a[1];fl[28]=258,revfl[258]=28;var _b=freb(fdeb,0);var fd=_b[0];var revfd=_b[1];var rev=new u16(32768);for(i=0;i<32768;++i){x=(i&43690)>>>1|(i&21845)<<1;x=(x&52428)>>>2|(x&13107)<<2;x=(x&61680)>>>4|(x&3855)<<4;rev[i]=((x&65280)>>>8|(x&255)<<8)>>>1}var x;var i;var hMap=function(cd,mb,r){var s=cd.length;var i2=0;var l=new u16(mb);for(;i2<s;++i2){if(cd[i2])++l[cd[i2]-1]}var le=new u16(mb);for(i2=0;i2<mb;++i2){le[i2]=le[i2-1]+l[i2-1]<<1}var co;if(r){co=new u16(1<<mb);var rvb=15-mb;for(i2=0;i2<s;++i2){if(cd[i2]){var sv=i2<<4|cd[i2];var r_1=mb-cd[i2];var v=le[cd[i2]-1]++<<r_1;for(var m=v|(1<<r_1)-1;v<=m;++v){co[rev[v]>>>rvb]=sv}}}}else{co=new u16(s);for(i2=0;i2<s;++i2){if(cd[i2]){co[i2]=rev[le[cd[i2]-1]++]>>>15-cd[i2]}}}return co};var flt=new u8(288);for(i=0;i<144;++i)flt[i]=8;var i;for(i=144;i<256;++i)flt[i]=9;var i;for(i=256;i<280;++i)flt[i]=7;var i;for(i=280;i<288;++i)flt[i]=8;var i;var fdt=new u8(32);for(i=0;i<32;++i)fdt[i]=5;var i;var flrm=hMap(flt,9,1);var fdrm=hMap(fdt,5,1);var max=function(a){var m=a[0];for(var i2=1;i2<a.length;++i2){if(a[i2]>m)m=a[i2]}return m};var bits=function(d,p,m){var o=p/8|0;return(d[o]|d[o+1]<<8)>>(p&7)&m};var bits16=function(d,p){var o=p/8|0;return(d[o]|d[o+1]<<8|d[o+2]<<16)>>(p&7)};var shft=function(p){return(p+7)/8|0};var slc=function(v,s,e){if(s==null||s<0)s=0;if(e==null||e>v.length)e=v.length;var n=new(v.BYTES_PER_ELEMENT==2?u16:v.BYTES_PER_ELEMENT==4?u32:u8)(e-s);n.set(v.subarray(s,e));return n};var ec=["unexpected EOF","invalid block type","invalid length/literal","invalid distance","stream finished","no stream handler",,"no callback","invalid UTF-8 data","extra field too long","date not in range 1980-2099","filename too long","stream finishing","invalid zip data"];var err=function(ind,msg,nt){var e=new Error(msg||ec[ind]);e.code=ind;if(Error.captureStackTrace)Error.captureStackTrace(e,err);if(!nt)throw e;return e};var inflt=function(dat,buf,st){var sl=dat.length;if(!sl||st&&st.f&&!st.l)return buf||new u8(0);var noBuf=!buf||st;var noSt=!st||st.i;if(!st)st={};if(!buf)buf=new u8(sl*3);var cbuf=function(l2){var bl=buf.length;if(l2>bl){var nbuf=new u8(Math.max(bl*2,l2));nbuf.set(buf);buf=nbuf}};var final=st.f||0,pos=st.p||0,bt=st.b||0,lm=st.l,dm=st.d,lbt=st.m,dbt=st.n;var tbts=sl*8;do{if(!lm){final=bits(dat,pos,1);var type=bits(dat,pos+1,3);pos+=3;if(!type){var s=shft(pos)+4,l=dat[s-4]|dat[s-3]<<8,t=s+l;if(t>sl){if(noSt)err(0);break}if(noBuf)cbuf(bt+l);buf.set(dat.subarray(s,t),bt);st.b=bt+=l,st.p=pos=t*8,st.f=final;continue}else if(type==1)lm=flrm,dm=fdrm,lbt=9,dbt=5;else if(type==2){var hLit=bits(dat,pos,31)+257,hcLen=bits(dat,pos+10,15)+4;var tl=hLit+bits(dat,pos+5,31)+1;pos+=14;var ldt=new u8(tl);var clt=new u8(19);for(var i2=0;i2<hcLen;++i2){clt[clim[i2]]=bits(dat,pos+i2*3,7)}pos+=hcLen*3;var clb=max(clt),clbmsk=(1<<clb)-1;var clm=hMap(clt,clb,1);for(var i2=0;i2<tl;){var r=clm[bits(dat,pos,clbmsk)];pos+=r&15;var s=r>>>4;if(s<16){ldt[i2++]=s}else{var c=0,n=0;if(s==16)n=3+bits(dat,pos,3),pos+=2,c=ldt[i2-1];else if(s==17)n=3+bits(dat,pos,7),pos+=3;else if(s==18)n=11+bits(dat,pos,127),pos+=7;while(n--)ldt[i2++]=c}}var lt=ldt.subarray(0,hLit),dt=ldt.subarray(hLit);lbt=max(lt);dbt=max(dt);lm=hMap(lt,lbt,1);dm=hMap(dt,dbt,1)}else err(1);if(pos>tbts){if(noSt)err(0);break}}if(noBuf)cbuf(bt+131072);var lms=(1<<lbt)-1,dms=(1<<dbt)-1;var lpos=pos;for(;;lpos=pos){var c=lm[bits16(dat,pos)&lms],sym=c>>>4;pos+=c&15;if(pos>tbts){if(noSt)err(0);break}if(!c)err(2);if(sym<256)buf[bt++]=sym;else if(sym==256){lpos=pos,lm=null;break}else{var add=sym-254;if(sym>264){var i2=sym-257,b=fleb[i2];add=bits(dat,pos,(1<<b)-1)+fl[i2];pos+=b}var d=dm[bits16(dat,pos)&dms],dsym=d>>>4;if(!d)err(3);pos+=d&15;var dt=fd[dsym];if(dsym>3){var b=fdeb[dsym];dt+=bits16(dat,pos)&(1<<b)-1,pos+=b}if(pos>tbts){if(noSt)err(0);break}if(noBuf)cbuf(bt+131072);var end=bt+add;for(;bt<end;bt+=4){buf[bt]=buf[bt-dt];buf[bt+1]=buf[bt+1-dt];buf[bt+2]=buf[bt+2-dt];buf[bt+3]=buf[bt+3-dt]}bt=end}}st.l=lm,st.p=lpos,st.b=bt,st.f=final;if(lm)final=1,st.m=lbt,st.d=dm,st.n=dbt}while(!final);return bt==buf.length?buf:slc(buf,0,bt)};var et=new u8(0);var gzs=function(d){if(d[0]!=31||d[1]!=139||d[2]!=8)err(6,"invalid gzip data");var flg=d[3];var st=10;if(flg&4)st+=d[10]|(d[11]<<8)+2;for(var zs=(flg>>3&1)+(flg>>4&1);zs>0;zs-=!d[st++]);return st+(flg&2)};var gzl=function(d){var l=d.length;return(d[l-4]|d[l-3]<<8|d[l-2]<<16|d[l-1]<<24)>>>0};function gunzipSync(data,out){return inflt(data.subarray(gzs(data),-8),out||new u8(gzl(data)))}var td=typeof TextDecoder!="undefined"&&new TextDecoder();var tds=0;try{td.decode(et,{stream:true});tds=1}catch(e){}var gz_default=gunzipSync;var calculate_excerpt_region=(word_positions,excerpt_length)=>{if(word_positions.length===0){return 0}let words=[];for(const word of word_positions){words[word.location]=words[word.location]||0;words[word.location]+=word.balanced_score}if(words.length<=excerpt_length){return 0}let densest=words.slice(0,excerpt_length).reduce((partialSum,a)=>partialSum+a,0);let working_sum=densest;let densest_at=[0];for(let i2=0;i2<words.length;i2++){const boundary=i2+excerpt_length;working_sum+=(words[boundary]??0)-(words[i2]??0);if(working_sum>densest){densest=working_sum;densest_at=[i2]}else if(working_sum===densest&&densest_at[densest_at.length-1]===i2-1){densest_at.push(i2)}}let midpoint=densest_at[Math.floor(densest_at.length/2)];return midpoint};var build_excerpt=(content,start,length,locations,not_before,not_from)=>{let is_zws_delimited=content.includes("\u200B");let fragment_words=[];if(is_zws_delimited){fragment_words=content.split("\u200B")}else{fragment_words=content.split(/[\r\n\s]+/g)}for(let word of locations){if(fragment_words[word]?.startsWith(`<mark>`)){continue}fragment_words[word]=`<mark>${fragment_words[word]}</mark>`}let endcap=not_from??fragment_words.length;let startcap=not_before??0;if(endcap-startcap<length){length=endcap-startcap}if(start+length>endcap){start=endcap-length}if(start<startcap){start=startcap}return fragment_words.slice(start,start+length).join(is_zws_delimited?"":" ").trim()};var calculate_sub_results=(fragment,desired_excerpt_length)=>{const anchors=fragment.anchors.filter((a)=>/h\d/i.test(a.element)&&a.text?.length&&/\S/.test(a.text)).sort((a,b)=>a.location-b.location);const results=[];let current_anchor_position=0;let current_anchor={title:fragment.meta["title"],url:fragment.url,weighted_locations:[],locations:[],excerpt:""};const add_result=(end_range)=>{if(current_anchor.locations.length){const relative_weighted_locations=current_anchor.weighted_locations.map((l)=>{return{weight:l.weight,balanced_score:l.balanced_score,location:l.location-current_anchor_position}});const excerpt_start=calculate_excerpt_region(relative_weighted_locations,desired_excerpt_length)+current_anchor_position;const excerpt_length=end_range?Math.min(end_range-excerpt_start,desired_excerpt_length):desired_excerpt_length;current_anchor.excerpt=build_excerpt(fragment.raw_content??"",excerpt_start,excerpt_length,current_anchor.locations,current_anchor_position,end_range);results.push(current_anchor)}};for(let word of fragment.weighted_locations){if(!anchors.length||word.location<anchors[0].location){current_anchor.weighted_locations.push(word);current_anchor.locations.push(word.location)}else{let next_anchor=anchors.shift();add_result(next_anchor.location);while(anchors.length&&word.location>=anchors[0].location){next_anchor=anchors.shift()}let anchored_url=fragment.url;try{const url_is_fq=/^((https?:)?\/\/)/.test(anchored_url);if(url_is_fq){let fq_url=new URL(anchored_url);fq_url.hash=next_anchor.id;anchored_url=fq_url.toString()}else{if(!/^\//.test(anchored_url)){anchored_url=`/${anchored_url}`}let fq_url=new URL(`https://example.com${anchored_url}`);fq_url.hash=next_anchor.id;anchored_url=fq_url.toString().replace(/^https:\/\/example.com/,"")}}catch(e){console.error(`Pagefind: Couldn't process ${anchored_url} for a search result`)}current_anchor_position=next_anchor.location;current_anchor={title:next_anchor.text,url:anchored_url,anchor:next_anchor,weighted_locations:[word],locations:[word.location],excerpt:""}}}add_result(anchors[0]?.location);return results};var asyncSleep=async(ms=100)=>{return new Promise((r)=>setTimeout(r,ms))};var PagefindInstance=class{constructor(opts={}){this.version=pagefind_version;this.backend=wasm_bindgen;this.decoder=new TextDecoder("utf-8");this.wasm=null;this.basePath=opts.basePath||"/pagefind/";this.primary=opts.primary||false;if(this.primary&&!opts.basePath){this.initPrimary()}if(/[^\/]$/.test(this.basePath)){this.basePath=`${this.basePath}/`}if(window?.location?.origin&&this.basePath.startsWith(window.location.origin)){this.basePath=this.basePath.replace(window.location.origin,"")}this.baseUrl=opts.baseUrl||this.defaultBaseUrl();if(!/^(\/|https?:\/\/)/.test(this.baseUrl)){this.baseUrl=`/${this.baseUrl}`}this.indexWeight=opts.indexWeight??1;this.excerptLength=opts.excerptLength??30;this.mergeFilter=opts.mergeFilter??{};this.ranking=opts.ranking;this.highlightParam=opts.highlightParam??null;this.loaded_chunks={};this.loaded_filters={};this.loaded_fragments={};this.raw_ptr=null;this.searchMeta=null;this.languages=null}initPrimary(){let derivedBasePath=import.meta.url.match(/^(.*\/)pagefind.js.*$/)?.[1];if(derivedBasePath){this.basePath=derivedBasePath}else{console.warn(["Pagefind couldn't determine the base of the bundle from the import path. Falling back to the default.","Set a basePath option when initialising Pagefind to ignore this message."].join("\n"))}}defaultBaseUrl(){let default_base=this.basePath.match(/^(.*\/)_?pagefind/)?.[1];return default_base||"/"}async options(options2){const opts=["basePath","baseUrl","indexWeight","excerptLength","mergeFilter","highlightParam","ranking"];for(const[k,v]of Object.entries(options2)){if(k==="mergeFilter"){let filters2=this.stringifyFilters(v);let ptr=await this.getPtr();this.raw_ptr=this.backend.add_synthetic_filter(ptr,filters2)}else if(k==="ranking"){await this.set_ranking(options2.ranking)}else if(opts.includes(k)){if(k==="basePath"&&typeof v==="string")this.basePath=v;if(k==="baseUrl"&&typeof v==="string")this.baseUrl=v;if(k==="indexWeight"&&typeof v==="number")this.indexWeight=v;if(k==="excerptLength"&&typeof v==="number")this.excerptLength=v;if(k==="mergeFilter"&&typeof v==="object")this.mergeFilter=v;if(k==="highlightParam"&&typeof v==="string")this.highlightParam=v}else{console.warn(`Unknown Pagefind option ${k}. Allowed options: [${opts.join(", ")}]`)}}}decompress(data,file="unknown file"){if(this.decoder.decode(data.slice(0,12))==="pagefind_dcd"){return data.slice(12)}data=gz_default(data);if(this.decoder.decode(data.slice(0,12))!=="pagefind_dcd"){console.error(`Decompressing ${file} appears to have failed: Missing signature`);return data}return data.slice(12)}async set_ranking(ranking){if(!ranking)return;let rankingWeights={term_similarity:ranking.termSimilarity??null,page_length:ranking.pageLength??null,term_saturation:ranking.termSaturation??null,term_frequency:ranking.termFrequency??null};let ptr=await this.getPtr();this.raw_ptr=this.backend.set_ranking_weights(ptr,JSON.stringify(rankingWeights))}async init(language,opts){await this.loadEntry();let index=this.findIndex(language);let lang_wasm=index.wasm?index.wasm:"unknown";let resources=[this.loadMeta(index.hash)];if(opts.load_wasm===true){resources.push(this.loadWasm(lang_wasm))}await Promise.all(resources);this.raw_ptr=this.backend.init_pagefind(new Uint8Array(this.searchMeta));if(Object.keys(this.mergeFilter)?.length){let filters2=this.stringifyFilters(this.mergeFilter);let ptr=await this.getPtr();this.raw_ptr=this.backend.add_synthetic_filter(ptr,filters2)}if(this.ranking){await this.set_ranking(this.ranking)}}async loadEntry(){try{let entry_response=await fetch(`${this.basePath}pagefind-entry.json?ts=${Date.now()}`);let entry_json=await entry_response.json();this.languages=entry_json.languages;if(entry_json.version!==this.version){if(this.primary){console.warn(["Pagefind JS version doesn't match the version in your search index.",`Pagefind JS: ${this.version}. Pagefind index: ${entry_json.version}`,"If you upgraded Pagefind recently, you likely have a cached pagefind.js file.","If you encounter any search errors, try clearing your cache."].join("\n"))}else{console.warn(["Merging a Pagefind index from a different version than the main Pagefind instance.",`Main Pagefind JS: ${this.version}. Merged index (${this.basePath}): ${entry_json.version}`,"If you encounter any search errors, make sure that both sites are running the same version of Pagefind."].join("\n"))}}}catch(e){console.error(`Failed to load Pagefind metadata:
 ${e?.toString()}`);throw new Error("Failed to load Pagefind metadata")}}findIndex(language){if(this.languages){let index=this.languages[language];if(index)return index;index=this.languages[language.split("-")[0]];if(index)return index;let topLang=Object.values(this.languages).sort((a,b)=>b.page_count-a.page_count);if(topLang[0])return topLang[0]}throw new Error("Pagefind Error: No language indexes found.")}async loadMeta(index){try{let compressed_resp=await fetch(`${this.basePath}pagefind.${index}.pf_meta`);let compressed_meta=await compressed_resp.arrayBuffer();this.searchMeta=this.decompress(new Uint8Array(compressed_meta),"Pagefind metadata")}catch(e){console.error(`Failed to load the meta index:
 ${e?.toString()}`)}}async loadWasm(language){try{const wasm_url=`${this.basePath}wasm.${language}.pagefind`;let compressed_resp=await fetch(wasm_url);let compressed_wasm=await compressed_resp.arrayBuffer();const final_wasm=this.decompress(new Uint8Array(compressed_wasm),"Pagefind WebAssembly");if(!final_wasm){throw new Error("No WASM after decompression")}this.wasm=await this.backend(final_wasm)}catch(e){console.error(`Failed to load the Pagefind WASM:
 ${e?.toString()}`);throw new Error(`Failed to load the Pagefind WASM:
diff --git a/pagefind/wasm.en.pagefind b/pagefind/wasm.en.pagefind
index efdb16ff..897cd6b5 100644
Binary files a/pagefind/wasm.en.pagefind and b/pagefind/wasm.en.pagefind differ
diff --git a/pagefind/wasm.unknown.pagefind b/pagefind/wasm.unknown.pagefind
index 82dba712..3ee72c92 100644
Binary files a/pagefind/wasm.unknown.pagefind and b/pagefind/wasm.unknown.pagefind differ
diff --git a/posts/bucketlist/index.html b/posts/bucketlist/index.html
index df18c459..2a430864 100644
--- a/posts/bucketlist/index.html
+++ b/posts/bucketlist/index.html
@@ -1,4 +1,4 @@
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+<!DOCTYPE html><html lang="en"> <head><!-- Global Metadata --><meta charset="utf-8"><meta name="viewport" content="width=device-width,initial-scale=1"><link rel="icon" type="image/icon" href="/favicon.ico"><meta name="generator" content="Astro v5.1.1"><!-- Canonical URL --><link rel="canonical" href="https://rezvan.xyz/posts/bucketlist/"><!-- Primary Meta Tags --><title>My personal bucket list | rezarezvan.com</title><meta name="title" content="My personal bucket list | rezarezvan.com"><meta name="description"><!-- Open Graph / Facebook --><meta property="og:type" content="website"><meta property="og:url" content="https://rezvan.xyz/posts/bucketlist/"><meta property="og:title" content="My personal bucket list | rezarezvan.com"><meta property="og:description"><meta property="og:image" content="https://rezvan.xyz/favicon.ico"><!-- Twitter --><meta property="twitter:card" content="summary_large_image"><meta property="twitter:url" content="https://rezvan.xyz/posts/bucketlist/"><meta property="twitter:title" content="My personal bucket list | rezarezvan.com"><meta property="twitter:description"><meta property="twitter:image" content="https://rezvan.xyz/favicon.ico"><!-- PageFind --><link href="/pagefind/pagefind-ui.css" rel="stylesheet"><script src="/pagefind/pagefind-ui.js"></script><!-- KaTeX support --><link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.15/dist/katex.min.css" integrity="sha384-Htz9HMhiwV8GuQ28Xr9pEs1B4qJiYu/nYLLwlDklR53QibDfmQzi7rYxXhMH/5/u" crossorigin="anonymous"><script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.15/dist/katex.min.js" integrity="sha384-bxmi2jLGCvnsEqMuYLKE/KsVCxV3PqmKeK6Y6+lmNXBry6+luFkEOsmp5vD9I/7+" crossorigin="anonymous"></script><script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.15/dist/contrib/auto-render.min.js" integrity="sha384-hCXGrW6PitJEwbkoStFjeJxv+fSOOQKOPbJxSfM6G5sWZjAyWhXiTIIAmQqnlLlh" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script><!-- inline KaTeX --><script>
     function renderKaTeX() {
         if (typeof renderMathInElement !== "undefined") {
             renderMathInElement(document.body, {
@@ -214,8 +214,8 @@
     document.addEventListener("DOMContentLoaded", () => init());
     document.addEventListener("astro:after-swap", () => init());
     preloadTheme();
-</script><link rel="stylesheet" href="/_astro/_subject_.CbuzD2Qq.css">
-<link rel="stylesheet" href="/_astro/index.CFKFE0Zk.css">
+</script><link rel="stylesheet" href="/_astro/_subject_.BUximwJU.css">
+<link rel="stylesheet" href="/_astro/index.CxbSBppY.css">
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@@ -239,7 +239,7 @@
 <li>Help someone achieve their dreams</li>
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@@ -250,8 +250,263 @@ <h3 id="the-neuron">The Neuron</h3>
 Each input $x_j$ is scaled by an associated weight denoted as $w_j$. The neuron also has a special input called the bias,
 $b$.</p>
 <p>The neuron has two stages it goes through, <strong>summation</strong> and <strong>activation</strong>.</p>
-<p><img src="/images/posts/neuron.png" alt="neuron">
-<strong>Figure 1:</strong> A single neuron with <em>n</em> inputs and one output, showcasing the summation and activation components.</p>
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+            .math {
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+                display: block;
+                margin: auto;
+                width: 85%;
+                height: auto;
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+            .math text {
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+<p><strong>Figure 1:</strong> A single neuron with <em>n</em> inputs and one output, showcasing the summation and activation components.</p>
 <p>The summation stage is where the neuron calculates the <strong>weighted sum</strong> of the inputs and the bias:
 $$
 \begin{equation}
@@ -287,8 +542,318 @@ <h3 id="the-network">The Network</h3>
 <p>A <em>layer</em> is a collection of neurons, stacked on top of each other.
 Very often when we are referring to a layer, are we referring to a <em>fully connected layer</em>, where each neuron in the layer is connected to all the neurons in the previous layer.</p>
 <p>In the case of a network, we can now talk about the input layer and the output layer.</p>
-<p><img src="/images/posts/nn.png" alt="nn">
-<strong>Figure 2:</strong> A simple neural network with one hidden layer.</p>
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+<path fill-rule="nonzero" fill="currentColor" fill-opacity="1" class="glyph" stroke-width="0.99628" stroke-linecap="butt" stroke-linejoin="miter" stroke="currentColor" stroke-opacity="1" stroke-miterlimit="10" d="M 7.084877 0.00117125 L 1.608315 2.071484 L 3.424721 0.00117125 L 1.608315 -2.069141 Z M 7.084877 0.00117125 " transform="matrix(1, 0, 0, -1, 305.90731, 243.98164)"></path>
+</svg>
+</div>
+<p><strong>Figure 2:</strong> A simple neural network with one hidden layer.</p>
 <p>As we see in the picture, we now have multiple neurons with numerous inter-neuron connections, along with multiple outputs.</p>
 <p>The matrix-vector equation,
 $$
@@ -521,7 +1086,7 @@ <h1 id="conclusion">Conclusion</h1>
 <p><a href="https://ieeexplore.ieee.org/document/6773024">Claude E. Shannon, “A mathematical theory of communication.”</a> <a href="#user-content-fnref-5" data-footnote-backref="" aria-label="Back to reference 5" class="data-footnote-backref">↩</a></p>
 </li>
 </ol>
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diff --git a/posts/editor/index.html b/posts/editor/index.html
index 03038c29..72b3f6bf 100644
--- a/posts/editor/index.html
+++ b/posts/editor/index.html
@@ -1,4 +1,4 @@
-<!DOCTYPE html><html lang="en"> <head><!-- Global Metadata --><meta charset="utf-8"><meta name="viewport" content="width=device-width,initial-scale=1"><link rel="icon" type="image/icon" href="/favicon.ico"><meta name="generator" content="Astro v5.0.5"><!-- Canonical URL --><link rel="canonical" href="https://rezvan.xyz/posts/editor/"><!-- Primary Meta Tags --><title>Vim-like editor | rezarezvan.com</title><meta name="title" content="Vim-like editor | rezarezvan.com"><meta name="description"><!-- Open Graph / Facebook --><meta property="og:type" content="website"><meta property="og:url" content="https://rezvan.xyz/posts/editor/"><meta property="og:title" content="Vim-like editor | rezarezvan.com"><meta property="og:description"><meta property="og:image" content="https://rezvan.xyz/favicon.ico"><!-- Twitter --><meta property="twitter:card" content="summary_large_image"><meta property="twitter:url" content="https://rezvan.xyz/posts/editor/"><meta property="twitter:title" content="Vim-like editor | rezarezvan.com"><meta property="twitter:description"><meta property="twitter:image" content="https://rezvan.xyz/favicon.ico"><!-- PageFind --><link href="/pagefind/pagefind-ui.css" rel="stylesheet"><script src="/pagefind/pagefind-ui.js"></script><!-- KaTeX support --><link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.15/dist/katex.min.css" integrity="sha384-Htz9HMhiwV8GuQ28Xr9pEs1B4qJiYu/nYLLwlDklR53QibDfmQzi7rYxXhMH/5/u" crossorigin="anonymous"><script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.15/dist/katex.min.js" integrity="sha384-bxmi2jLGCvnsEqMuYLKE/KsVCxV3PqmKeK6Y6+lmNXBry6+luFkEOsmp5vD9I/7+" crossorigin="anonymous"></script><script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.15/dist/contrib/auto-render.min.js" integrity="sha384-hCXGrW6PitJEwbkoStFjeJxv+fSOOQKOPbJxSfM6G5sWZjAyWhXiTIIAmQqnlLlh" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script><!-- inline KaTeX --><script>
+<!DOCTYPE html><html lang="en"> <head><!-- Global Metadata --><meta charset="utf-8"><meta name="viewport" content="width=device-width,initial-scale=1"><link rel="icon" type="image/icon" href="/favicon.ico"><meta name="generator" content="Astro v5.1.1"><!-- Canonical URL --><link rel="canonical" href="https://rezvan.xyz/posts/editor/"><!-- Primary Meta Tags --><title>Vim-like editor | rezarezvan.com</title><meta name="title" content="Vim-like editor | rezarezvan.com"><meta name="description"><!-- Open Graph / Facebook --><meta property="og:type" content="website"><meta property="og:url" content="https://rezvan.xyz/posts/editor/"><meta property="og:title" content="Vim-like editor | rezarezvan.com"><meta property="og:description"><meta property="og:image" content="https://rezvan.xyz/favicon.ico"><!-- Twitter --><meta property="twitter:card" content="summary_large_image"><meta property="twitter:url" content="https://rezvan.xyz/posts/editor/"><meta property="twitter:title" content="Vim-like editor | rezarezvan.com"><meta property="twitter:description"><meta property="twitter:image" content="https://rezvan.xyz/favicon.ico"><!-- PageFind --><link href="/pagefind/pagefind-ui.css" rel="stylesheet"><script src="/pagefind/pagefind-ui.js"></script><!-- KaTeX support --><link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.15/dist/katex.min.css" integrity="sha384-Htz9HMhiwV8GuQ28Xr9pEs1B4qJiYu/nYLLwlDklR53QibDfmQzi7rYxXhMH/5/u" crossorigin="anonymous"><script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.15/dist/katex.min.js" integrity="sha384-bxmi2jLGCvnsEqMuYLKE/KsVCxV3PqmKeK6Y6+lmNXBry6+luFkEOsmp5vD9I/7+" crossorigin="anonymous"></script><script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.15/dist/contrib/auto-render.min.js" integrity="sha384-hCXGrW6PitJEwbkoStFjeJxv+fSOOQKOPbJxSfM6G5sWZjAyWhXiTIIAmQqnlLlh" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script><!-- inline KaTeX --><script>
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@@ -214,8 +214,8 @@
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     preloadTheme();
-</script><link rel="stylesheet" href="/_astro/_subject_.CbuzD2Qq.css">
-<link rel="stylesheet" href="/_astro/index.CFKFE0Zk.css">
+</script><link rel="stylesheet" href="/_astro/_subject_.BUximwJU.css">
+<link rel="stylesheet" href="/_astro/index.CxbSBppY.css">
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decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> chalmers </a> <span>/</span> <a href="/cityu" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> cityu </a> <span>/</span> <a href="/pdf/cv/cv.pdf" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> cv </a> <span>/</span> <button id="magnifying-glass" aria-label="Search" class="flex items-center rounded border border-black/15 bg-neutral-100 px-2 py-1 text-xs transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:bg-neutral-900 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg height="16" stroke-linejoin="round" viewBox="0 0 16 16" width="16" style="color: currentcolor;"> <path fill-rule="evenodd" clip-rule="evenodd" d="M3.5 7C3.5 5.067 5.067 3.5 7 3.5C8.933 3.5 10.5 5.067 10.5 7C10.5 7.88461 10.1718 8.69256 9.63058 9.30876L9.30876 9.63058C8.69256 10.1718 7.88461 10.5 7 10.5C5.067 10.5 3.5 8.933 3.5 7ZM9.96544 11.0261C9.13578 11.6382 8.11014 12 7 12C4.23858 12 2 9.76142 2 7C2 4.23858 4.23858 2 7 2C9.76142 2 12 4.23858 12 7C12 8.11014 11.6382 9.13578 11.0261 9.96544L14.0303 12.9697L14.5607 13.5L13.5 14.5607L12.9697 14.0303L9.96544 11.0261Z" fill="currentColor"></path> </svg>
@@ -232,7 +232,7 @@
 <p>Here are some screenshots for preview.</p>
 <p><img src="/images/posts/screenshot1.png" alt="Screenshot_1">
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+<div class="font-base text-sm"> 1 min read </div> </div> <h1 class="animate text-3xl font-semibold text-black dark:text-white"> Initial post </h1> </div> <article class="animate"> <p>This is just an initial post - I’ll mainly write about things I find fascinating/interesting on this site :).</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/posts/bucketlist" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> My personal bucket list </div> </a> <div class="invisible"></div> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -232,7 +232,7 @@
 <p>The project I’ve liked the best so far is a program that visualizes <a href="https://en.wikipedia.org/wiki/Fourier_series">Fourier Series</a> - In this project, I wrote the math as well so that was fun.
 Here’s a GIF to show the output:</p>
 <p><img src="/images/posts/fourier.gif" alt="fourier"></p>
-<p>I’m glad I’ve started to learn Julia, it seems like a nice language for visual and data related projects. Definitely a language I will continue to learn and explore.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/posts/programming_principles" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Programming Principles </div> </a> <a href="/posts/editor" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Vim-like editor </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>I’m glad I’ve started to learn Julia, it seems like a nice language for visual and data related projects. Definitely a language I will continue to learn and explore.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/posts/programming_principles" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Programming Principles </div> </a> <a href="/posts/editor" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Vim-like editor </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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diff --git a/posts/links/index.html b/posts/links/index.html
index a4041473..ec080973 100644
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+++ b/posts/links/index.html
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@@ -241,7 +241,7 @@
 <li><a href="https://yacine.ca">yacine.ca</a></li>
 <li><a href="https://fullnitrous.com">fullnitrous.com</a></li>
 <li><a href="https://nat.org">nat.org</a></li>
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@@ -256,7 +256,7 @@
 <hr>
 <p>This is the first time I write something like this.
 I got inspired by <a href="https://tommytrinh.me/journal/sit-straight">this post</a> and, it hit close to home.</p>
-<p>I hope you enjoyed it.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/posts/uncertainty" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Uncertainty makes the soul </div> </a> <a href="/posts/links" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Links </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>I hope you enjoyed it.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <a href="/posts/uncertainty" class="group relative flex flex-nowrap rounded-lg border border-black/15 px-4 py-3 pl-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Uncertainty makes the soul </div> </a> <a href="/posts/links" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Links </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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@@ -291,7 +291,7 @@ <h4 id="ergonomics">Ergonomics</h4>
 <h4 id="summary">Summary</h4>
 <p>The common theme in this post is that, trying out new stuff and finding what fits you, and really sticking to those things -
 is what makes a great engineer in my eyes.
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@@ -223,9 +223,9 @@
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-Last modified:  <time datetime="2024-12-20T15:34:53.000Z"> December 20, 2024 </time> </div> 
+Last modified:  <time datetime="2024-12-21T18:04:34.000Z"> December 22, 2024 </time> </div> 
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-<div class="font-base text-sm"> 7 min read </div> </div> <h1 class="animate text-3xl font-semibold text-black dark:text-white"> Rezvan Explains: Classical Machine Learning </h1> </div> <details open class="animate rounded-lg border border-black/15 dark:border-white/20" data-astro-cid-xvrfupwn> <summary data-astro-cid-xvrfupwn>Table of Contents</summary> <nav class="" data-astro-cid-xvrfupwn> <ul class="py-3" data-astro-cid-xvrfupwn> <li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#preqrequisites-and-notation" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Preqrequisites and Notation </a>  </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#introduction-what-why-and-how" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Introduction: What, Why and How? </a> <ul class="translate-x-3"> <li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#statistics-vs-machine-learning" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Statistics VS. Machine Learning </a>  </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#humble-beginnings" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Humble Beginnings </a>  </li> </ul> </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#different-types-of-learning" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Different Types of Learning </a> <ul class="translate-x-3"> <li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#supervised-learning" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Supervised Learning </a>  </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#the-classification-task" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> The Classification Task </a>  </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#the-classification-learning-problem" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> The Classification Learning Problem </a> <ul class="translate-x-3"> <li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#metrics" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Metrics </a>  </li> </ul> </li> </ul> </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#footnote-label" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Footnotes </a>  </li> </ul> </nav> </details> <article class="animate"> <p><img src="/images/posts/re_header.jpg" alt=""></p>
+<div class="font-base text-sm"> 7 min read </div> </div> <h1 class="animate text-3xl font-semibold text-black dark:text-white"> Rezvan Explains: Classical Machine Learning </h1> </div> <details open class="animate rounded-lg border border-black/15 dark:border-white/20" data-astro-cid-xvrfupwn> <summary data-astro-cid-xvrfupwn>Table of Contents</summary> <nav class="" data-astro-cid-xvrfupwn> <ul class="py-3" data-astro-cid-xvrfupwn> <li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#preqrequisites-and-notation" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Preqrequisites and Notation </a>  </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#introduction-what-why-and-how" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Introduction: What, Why and How? </a> <ul class="translate-x-3"> <li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#statistics-vs-machine-learning" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Statistics VS. Machine Learning </a>  </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#humble-beginnings" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Humble Beginnings </a>  </li> </ul> </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#different-types-of-learning" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Different Types of Learning </a> <ul class="translate-x-3"> <li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#supervised-learning" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Supervised Learning </a> <ul class="translate-x-3"> <li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#the-classification-task" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> The Classification Task </a>  </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#the-classification-learning-problem" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> The Classification Learning Problem </a> <ul class="translate-x-3"> <li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#metrics" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Metrics </a>  </li> </ul> </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#different-approaches" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Different Approaches </a> <ul class="translate-x-3"> <li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#generative-models" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Generative Models </a>  </li> </ul> </li> </ul> </li> </ul> </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#footnote-label" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Footnotes </a>  </li> </ul> </nav> </details> <article class="animate"> <p><img src="/images/posts/re_header.jpg" alt=""></p>
 <p style="font-weight:bold; text-align:center;"> Rezvan Explains: Classical Machine Learning</p>
 <p style="font-size:15px; font-weight:italic; text-align:center;"> Veni, disce mecum </p>
 <p>As of writing this, last night as I was going to sleep, I was lying in bed and thought about the future.
@@ -317,7 +317,7 @@ <h3 id="supervised-learning">Supervised Learning</h3>
 \end{equation}
 $$</p>
 <p>where $\mathbf{X}$ is the input space and $\mathbf{Y}$ is the output space, we want to find the <em>best</em> function $f$ that maps $\mathbf{X}$ to $\mathbf{Y}$.</p>
-<h3 id="the-classification-task">The Classification Task</h3>
+<h4 id="the-classification-task">The Classification Task</h4>
 <p>The best way to understand supervised learning is through the <strong>classification task</strong> and <em>Fisher’s Iris dataset</em>. <sup><a href="#user-content-fn-5" id="user-content-fnref-5" data-footnote-ref="" aria-describedby="footnote-label">5</a></sup></p>
 <p>In Fisher’s Iris dataset we have 150 samples of input-output pairs.
 The input is a vector with four <strong>features</strong> — sepal length, sepal width, petal length, petal width — the output is the <strong>species</strong> of the iris flower.</p>
@@ -335,14 +335,14 @@ <h3 id="the-classification-task">The Classification Task</h3>
 <blockquote>
 <p>Given a feature vector $\mathbf{x} \in \mathbf{X} = \mathbb{R}^N$ that describes an object that belongs to one of $C$ classes from the set $\mathbf{Y} = \{ 1, 2, \ldots, C \}$, predict the class label $y \in \mathbf{Y}$.</p>
 </blockquote>
-<h3 id="the-classification-learning-problem">The Classification Learning Problem</h3>
+<h4 id="the-classification-learning-problem">The Classification Learning Problem</h4>
 <p>Now that we have defined the classification task, let’s define the classification learning problem,</p>
 <blockquote>
 <p>Given a dataset of example pairs $\mathcal{D} = \{ (\mathbf{x}^{(i)}, y^{(i)}), i = 1, \ldots, M \}$
 where $\mathbf{x}^{(i)} \in \mathbf{X} = \mathbb{R}^N$ is a feature vector and $y^{(i)} \in \mathbf{Y} = \{1, \ldots, C\}$ is the class label,
 learn a function $f: \mathbb{R}^N \mapsto \mathbf{Y}$ that accurately predicts the class label $y$ for any feature vector $\mathbf{x}$.</p>
 </blockquote>
-<h4 id="metrics">Metrics</h4>
+<h5 id="metrics">Metrics</h5>
 <p>To determine how well our function $f$ is doing, we need to define some (primal) metrics.</p>
 <p>Firstly, let’s define the <strong>indicator function</strong>,</p>
 <p>$$
@@ -374,6 +374,20 @@ <h4 id="metrics">Metrics</h4>
 \end{equation}
 $$</p>
 </blockquote>
+<h4 id="different-approaches">Different Approaches</h4>
+<p>But how do we solve the classification learning problem?
+We will go through different ways of approaching this problem.</p>
+<p>But I want to start of with the <strong>probabilistic approach</strong> first.</p>
+<h5 id="generative-models">Generative Models</h5>
+<p>We know that our dataset $\mathcal{D}$ consists of input-output pairs $(\mathbf{x}^{(i)}, y^{(i)})$.
+In the real dataset, we have a <strong>joint distribution</strong> $p(\mathbf{x}, y)$, this describes the probability of observing the pair $(\mathbf{x}, y)$.</p>
+<p>We can learn this joint distribution from the dataset.
+We know from <strong>Bayes’ Rule</strong> that,</p>
+<p>$$
+\begin{equation}
+p(\mathbf{x}, y) = p(y | \mathbf{x}) p(\mathbf{x}),
+\end{equation}
+$$</p>
 <section data-footnotes="" class="footnotes"><h2 class="sr-only" id="footnote-label">Footnotes</h2>
 <ol>
 <li id="user-content-fn-1">
@@ -392,7 +406,7 @@ <h4 id="metrics">Metrics</h4>
 <p><a href="https://en.wikipedia.org/wiki/Iris_flower_data_set">Wikipedia, Iris Flower Data Set</a> <a href="#user-content-fnref-5" data-footnote-backref="" aria-label="Back to reference 5" class="data-footnote-backref">↩</a></p>
 </li>
 </ol>
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diff --git a/posts/uncertainty/index.html b/posts/uncertainty/index.html
index fda5014f..75631c3f 100644
--- a/posts/uncertainty/index.html
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@@ -242,7 +242,7 @@
 <p>What makes something feel alive is a spectrum, a truly <a href="https://en.wikipedia.org/wiki/Chaos_theory">chaotic</a> system does not feel alive either.</p>
 <p>You can’t sense any patterns or familiarity, it is beyond our (current) comprehension.</p>
 <hr>
-<p>The sense of something feeling alive is a byproduct of a <a href="https://en.wikipedia.org/wiki/Entropy_(information_theory)">certain amount of uncertainty</a> in the system.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/posts/pause" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Never put your life on hold </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.BoThSDgl.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
+<p>The sense of something feeling alive is a byproduct of a <a href="https://en.wikipedia.org/wiki/Entropy_(information_theory)">certain amount of uncertainty</a> in the system.</p> <div class="mt-24"> <div class="grid grid-cols-2 gap-1.5 sm:gap-3"> <div class="invisible"></div> <a href="/posts/pause" class="group relative flex flex-grow flex-row-reverse flex-nowrap rounded-lg border border-black/15 px-4 py-4 pr-10 no-underline transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute right-2 top-1/2 size-5 -translate-y-1/2 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-3 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 19 12 12 19" class="-translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="flex items-center text-sm"> Never put your life on hold </div> </a> </div> </div> <div class="mt-24"> <div class="giscus"></div> <script data-astro-rerun src="https://giscus.app/client.js" data-repo="rezaarezvan/rezvan.xyz" data-repo-id="R_kgDOHvQr3w" data-category="General" data-category-id="DIC_kwDOHvQr384CiWVC" data-mapping="pathname" data-strict="0" data-reactions-enabled="1" data-emit-metadata="0" data-input-position="bottom" data-theme="preferred_color_scheme" data-lang="en" data-loading="lazy" crossorigin="anonymous" async></script> </div> </article> </div>  </main> <footer class="animate"> <div class="mx-auto max-w-screen-sm px-3"> <div class="relative"> <div class="absolute -top-12 right-0"> <button id="back-to-top" class="group relative flex w-fit flex-nowrap rounded border border-black/15 py-1.5 pl-8 pr-3 transition-colors duration-300 ease-in-out hover:bg-black/5 hover:text-black focus-visible:bg-black/5 focus-visible:text-black dark:border-white/20 dark:hover:bg-white/5 dark:hover:text-white dark:focus-visible:bg-white/5 dark:focus-visible:text-white"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="absolute left-2 top-1/2 size-4 -translate-y-1/2 rotate-90 fill-none stroke-current stroke-2"> <line x1="5" y1="12" x2="19" y2="12" class="translate-x-2 scale-x-0 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-hover:scale-x-100 group-focus-visible:translate-x-0 group-focus-visible:scale-x-100"></line> <polyline points="12 5 5 12 12 19" class="translate-x-1 transition-transform duration-300 ease-in-out group-hover:translate-x-0 group-focus-visible:translate-x-0"></polyline> </svg> <div class="text-sm">Back to top</div> </button> </div> </div> <div class="flex items-center justify-between"> <div>&copy; 2024 • rezarezvan.com</div> <div class="flex flex-wrap items-center gap-1.5"></div> </div> </div> </footer> <aside data-pagefind-ignore> <div id="backdrop" class="bg-[rgba(0, 0, 0, 0.5] invisible fixed left-0 top-0 z-50 flex h-screen w-full justify-center p-6 backdrop-blur-sm" data-astro-transition-persist="astro-3snakcvo-2"> <div id="pagefind-container" class="m-0 flex h-fit max-h-[80%] w-full max-w-screen-sm flex-col overflow-auto rounded border border-black/15 bg-neutral-100 p-2 px-4 py-3 shadow-lg dark:border-white/20 dark:bg-neutral-900"> <div id="search" class="pagefind-ui pagefind-init" data-pagefind-ui data-bundle-path="/pagefind/" data-ui-options="{&#34;showImages&#34;:false,&#34;excerptLength&#34;:15,&#34;resetStyles&#34;:false}"></div> <script type="module" src="/_astro/Search.astro_astro_type_script_index_0_lang.C4tRTXsn.js"></script> <div class="mr-2 pb-1 pt-4 text-right text-xs dark:prose-invert">
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-<?xml version="1.0" encoding="UTF-8"?><rss version="2.0"><channel><title>rezarezvan.com</title><description/><link>https://rezvan.xyz/</link><item><title>Uncertainty makes the soul</title><link>https://rezvan.xyz/posts/uncertainty/</link><guid isPermaLink="true">https://rezvan.xyz/posts/uncertainty/</guid><pubDate>Tue, 03 Dec 2024 00:00:00 GMT</pubDate></item><item><title>Part 9 - Discrete Systems</title><link>https://rezvan.xyz/cityu/bme3105/bme3105_9/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/bme3105/bme3105_9/</guid><pubDate>Fri, 22 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 5 - Multiple Linear Regression</title><link>https://rezvan.xyz/cityu/ma3518/ma3518_5/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/ma3518/ma3518_5/</guid><pubDate>Thu, 21 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 11 - High-Level and Low-Level Vision Applications</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_11/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_11/</guid><pubDate>Wed, 20 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 8 - Stability and Controller Design</title><link>https://rezvan.xyz/cityu/bme3105/bme3105_8/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/bme3105/bme3105_8/</guid><pubDate>Fri, 15 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 10 - Neural Networks and Deep Learning Part 2</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_10/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_10/</guid><pubDate>Wed, 13 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 10 - Future trends of Big Data</title><link>https://rezvan.xyz/cityu/is2021/is2021_10/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021_10/</guid><pubDate>Tue, 12 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 7 - State Space Realization</title><link>https://rezvan.xyz/cityu/bme3105/bme3105_7/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/bme3105/bme3105_7/</guid><pubDate>Fri, 08 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 4 - Simple Linear Regression</title><link>https://rezvan.xyz/cityu/ma3518/ma3518_4/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/ma3518/ma3518_4/</guid><pubDate>Thu, 07 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 9 - Neural Networks and Deep Learning</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_9/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_9/</guid><pubDate>Wed, 06 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 9 - NoSQL Data Management for Big Data</title><link>https://rezvan.xyz/cityu/is2021/is2021_9/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021_9/</guid><pubDate>Tue, 05 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 6 - State Space Approach</title><link>https://rezvan.xyz/cityu/bme3105/bme3105_6/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/bme3105/bme3105_6/</guid><pubDate>Fri, 01 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 7 - Thermal Actuators and Piezoresistivity</title><link>https://rezvan.xyz/cityu/mne3115/mne3115_7/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/mne3115/mne3115_7/</guid><pubDate>Fri, 01 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 8 - Principal Component Analysis</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_8/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_8/</guid><pubDate>Wed, 30 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 8 - Data Governance for BDA – Data Policies &amp; Processes</title><link>https://rezvan.xyz/cityu/is2021/is2021_8/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021_8/</guid><pubDate>Tue, 29 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 5 - Stability</title><link>https://rezvan.xyz/cityu/bme3105/bme3105_5/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/bme3105/bme3105_5/</guid><pubDate>Fri, 25 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 7 - The Expectation Maximization Algorithm &amp; Linear Dimensionality Reduction</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_7/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_7/</guid><pubDate>Wed, 23 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 6 - Elasticity</title><link>https://rezvan.xyz/cityu/mne3115/mne3115_6/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/mne3115/mne3115_6/</guid><pubDate>Fri, 18 Oct 2024 23:15:00 GMT</pubDate></item><item><title>Part 5 - Fabrication Techniques</title><link>https://rezvan.xyz/cityu/mne3115/mne3115_5/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/mne3115/mne3115_5/</guid><pubDate>Fri, 18 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 6 - Robust, Non-Linear Regression and Clustering</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_6/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_6/</guid><pubDate>Wed, 16 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 7 - Developing a Strategy for Integrating Big Data Analytics into the Enterprise</title><link>https://rezvan.xyz/cityu/is2021/is2021_7/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021_7/</guid><pubDate>Tue, 15 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 5 - Regression</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_5/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_5/</guid><pubDate>Wed, 09 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Never put your life on hold</title><link>https://rezvan.xyz/posts/pause/</link><guid isPermaLink="true">https://rezvan.xyz/posts/pause/</guid><pubDate>Fri, 04 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 4 - Time Respone</title><link>https://rezvan.xyz/cityu/bme3105/bme3105_4/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/bme3105/bme3105_4/</guid><pubDate>Fri, 04 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 4 - Etching</title><link>https://rezvan.xyz/cityu/mne3115/mne3115_4/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/mne3115/mne3115_4/</guid><pubDate>Fri, 04 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 4 - Duality and SVM</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_4/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_4/</guid><pubDate>Wed, 02 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 6 - Achieving Organizational Alignment for Big Data Analytics</title><link>https://rezvan.xyz/cityu/is2021/is2021_6/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021_6/</guid><pubDate>Tue, 01 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 3 - Modelling in Frequency Domain</title><link>https://rezvan.xyz/cityu/bme3105/bme3105_3/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/bme3105/bme3105_3/</guid><pubDate>Fri, 27 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 3 - Thin Film Growth and Deposition</title><link>https://rezvan.xyz/cityu/mne3115/mne3115_3/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/mne3115/mne3115_3/</guid><pubDate>Fri, 27 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 3 - Optimization and Convexity</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_3/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_3/</guid><pubDate>Wed, 25 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 5 - Developing Big Data Applications</title><link>https://rezvan.xyz/cityu/is2021/is2021_5/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021_5/</guid><pubDate>Tue, 24 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 4 - Big Data Tools and Techniques</title><link>https://rezvan.xyz/cityu/is2021/is2021_4/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021_4/</guid><pubDate>Sat, 21 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 2 - Photolithography</title><link>https://rezvan.xyz/cityu/mne3115/mne3115_2/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/mne3115/mne3115_2/</guid><pubDate>Fri, 20 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 3 - Confidence Interval and Hypothesis Testing</title><link>https://rezvan.xyz/cityu/ma3518/ma3518_3/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/ma3518/ma3518_3/</guid><pubDate>Thu, 19 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 3 - High-Performance Applications</title><link>https://rezvan.xyz/cityu/is2021/is2021_3/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021_3/</guid><pubDate>Tue, 17 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 2 - System Modelling</title><link>https://rezvan.xyz/cityu/bme3105/bme3105_2/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/bme3105/bme3105_2/</guid><pubDate>Fri, 13 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 2 - Basic Statistical Concepts and Tools</title><link>https://rezvan.xyz/cityu/ma3518/ma3518_2/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/ma3518/ma3518_2/</guid><pubDate>Thu, 12 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 2 - Generative VS. Discriminative Models</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_2/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_2/</guid><pubDate>Wed, 11 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 2 - Business Drivers for Big Data Analytics &amp; its related Business Problems</title><link>https://rezvan.xyz/cityu/is2021/is2021_2/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021_2/</guid><pubDate>Tue, 10 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction</title><link>https://rezvan.xyz/cityu/bme3105/bme3105/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/bme3105/bme3105/</guid><pubDate>Fri, 06 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction</title><link>https://rezvan.xyz/cityu/mne3115/mne3115/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/mne3115/mne3115/</guid><pubDate>Fri, 06 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction to R</title><link>https://rezvan.xyz/cityu/ma3518/ma3518/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/ma3518/ma3518/</guid><pubDate>Thu, 05 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction</title><link>https://rezvan.xyz/cityu/cs4487/cs4487/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487/</guid><pubDate>Wed, 04 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 1 - Evolution of Data Management</title><link>https://rezvan.xyz/cityu/is2021/is2021/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021/</guid><pubDate>Tue, 03 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Links</title><link>https://rezvan.xyz/posts/links/</link><guid isPermaLink="true">https://rezvan.xyz/posts/links/</guid><pubDate>Wed, 17 Jul 2024 00:00:00 GMT</pubDate></item><item><title>Part 9 - Machine Learning</title><link>https://rezvan.xyz/chalmers/dat565/dat565_9/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat565/dat565_9/</guid><pubDate>Tue, 20 Feb 2024 00:00:00 GMT</pubDate></item><item><title>Part 8 - Distance and network methods</title><link>https://rezvan.xyz/chalmers/dat565/dat565_8/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat565/dat565_8/</guid><pubDate>Tue, 13 Feb 2024 00:00:00 GMT</pubDate></item><item><title>Part 7 - Linear and logistic regression</title><link>https://rezvan.xyz/chalmers/dat565/dat565_7/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat565/dat565_7/</guid><pubDate>Tue, 06 Feb 2024 00:00:00 GMT</pubDate></item><item><title>Part 6 - Mathematical models</title><link>https://rezvan.xyz/chalmers/dat565/dat565_6/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat565/dat565_6/</guid><pubDate>Fri, 02 Feb 2024 00:00:00 GMT</pubDate></item><item><title>Part 5 - Statistical analysis</title><link>https://rezvan.xyz/chalmers/dat565/dat565_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat565/dat565_5/</guid><pubDate>Sat, 27 Jan 2024 00:00:00 GMT</pubDate></item><item><title>Part 4 - Data visualization</title><link>https://rezvan.xyz/chalmers/dat565/dat565_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat565/dat565_4/</guid><pubDate>Fri, 26 Jan 2024 00:00:00 GMT</pubDate></item><item><title>Part 3 - Data munging</title><link>https://rezvan.xyz/chalmers/dat565/dat565_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat565/dat565_3/</guid><pubDate>Tue, 23 Jan 2024 00:00:00 GMT</pubDate></item><item><title>Part 2 - Python tools for data science</title><link>https://rezvan.xyz/chalmers/dat565/dat565_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat565/dat565_2/</guid><pubDate>Fri, 19 Jan 2024 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction</title><link>https://rezvan.xyz/chalmers/dat565/dat565/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat565/dat565/</guid><pubDate>Tue, 16 Jan 2024 00:00:00 GMT</pubDate></item><item><title>Part 15 - Summary</title><link>https://rezvan.xyz/chalmers/ere103/ere103_summary/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_summary/</guid><pubDate>Sat, 30 Dec 2023 00:00:00 GMT</pubDate></item><item><title>Part 14 - Filters</title><link>https://rezvan.xyz/chalmers/ere103/ere103_14/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_14/</guid><pubDate>Thu, 07 Dec 2023 00:00:00 GMT</pubDate></item><item><title>Part 13 - Discretization</title><link>https://rezvan.xyz/chalmers/ere103/ere103_13/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_13/</guid><pubDate>Wed, 06 Dec 2023 00:00:00 GMT</pubDate></item><item><title>Part 12 - State feedback</title><link>https://rezvan.xyz/chalmers/ere103/ere103_12/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_12/</guid><pubDate>Tue, 05 Dec 2023 00:00:00 GMT</pubDate></item><item><title>Part 11 - Design of controllers (2)</title><link>https://rezvan.xyz/chalmers/ere103/ere103_11/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_11/</guid><pubDate>Tue, 28 Nov 2023 00:00:00 GMT</pubDate></item><item><title>Part 10 - Design of controllers</title><link>https://rezvan.xyz/chalmers/ere103/ere103_10/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_10/</guid><pubDate>Mon, 27 Nov 2023 00:00:00 GMT</pubDate></item><item><title>Part 9 - General controller structure</title><link>https://rezvan.xyz/chalmers/ere103/ere103_9/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_9/</guid><pubDate>Thu, 23 Nov 2023 00:00:00 GMT</pubDate></item><item><title>Part 8 - Stability</title><link>https://rezvan.xyz/chalmers/ere103/ere103_8/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_8/</guid><pubDate>Thu, 16 Nov 2023 00:00:00 GMT</pubDate></item><item><title>Part 7 - Bode plot</title><link>https://rezvan.xyz/chalmers/ere103/ere103_7/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_7/</guid><pubDate>Mon, 13 Nov 2023 00:00:00 GMT</pubDate></item><item><title>Part 6 - Space-state representation (2)</title><link>https://rezvan.xyz/chalmers/ere103/ere103_6/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_6/</guid><pubDate>Thu, 09 Nov 2023 00:00:00 GMT</pubDate></item><item><title>Part 5 - Space-state representation (1)</title><link>https://rezvan.xyz/chalmers/ere103/ere103_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_5/</guid><pubDate>Tue, 07 Nov 2023 00:00:00 GMT</pubDate></item><item><title>Part 4 - Models for mechanical systems</title><link>https://rezvan.xyz/chalmers/ere103/ere103_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_4/</guid><pubDate>Mon, 06 Nov 2023 00:00:00 GMT</pubDate></item><item><title>Part 3 - Controllers in the Laplace domain</title><link>https://rezvan.xyz/chalmers/ere103/ere103_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_3/</guid><pubDate>Sun, 05 Nov 2023 00:00:00 GMT</pubDate></item><item><title>Part 2 - Transfer functions</title><link>https://rezvan.xyz/chalmers/ere103/ere103_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_2/</guid><pubDate>Tue, 31 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction</title><link>https://rezvan.xyz/chalmers/ere103/ere103/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103/</guid><pubDate>Mon, 30 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 21 - Summary</title><link>https://rezvan.xyz/chalmers/lma017/lma017_summary/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_summary/</guid><pubDate>Thu, 19 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 20 - Divergence and Stokes&apos; Theorem</title><link>https://rezvan.xyz/chalmers/lma017/lma017_20/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_20/</guid><pubDate>Wed, 18 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 10 - Summary</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081_summary/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081_summary/</guid><pubDate>Sun, 15 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 19 - Surface integrals</title><link>https://rezvan.xyz/chalmers/lma017/lma017_19/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_19/</guid><pubDate>Wed, 11 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 18 - Green&apos;s Theorem</title><link>https://rezvan.xyz/chalmers/lma017/lma017_18/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_18/</guid><pubDate>Tue, 10 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 17 - Gradient theorem</title><link>https://rezvan.xyz/chalmers/lma017/lma017_17/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_17/</guid><pubDate>Wed, 04 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 16 - Vector fields</title><link>https://rezvan.xyz/chalmers/lma017/lma017_16/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_16/</guid><pubDate>Tue, 03 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 15 - Line integrals</title><link>https://rezvan.xyz/chalmers/lma017/lma017_15/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_15/</guid><pubDate>Sun, 01 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 9 - Laplace transform</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081_9/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081_9/</guid><pubDate>Thu, 28 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 14 - Curves</title><link>https://rezvan.xyz/chalmers/lma017/lma017_14/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_14/</guid><pubDate>Wed, 27 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 13 - The Jacobian</title><link>https://rezvan.xyz/chalmers/lma017/lma017_13/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_13/</guid><pubDate>Tue, 26 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 8 - Signal reconstruction</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081_8/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081_8/</guid><pubDate>Mon, 25 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 12 - Change of variables</title><link>https://rezvan.xyz/chalmers/lma017/lma017_12/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_12/</guid><pubDate>Fri, 22 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 7 - Nyquist-Shannon sampling theorem</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081_7/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081_7/</guid><pubDate>Thu, 21 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 11 - General regions (2)</title><link>https://rezvan.xyz/chalmers/lma017/lma017_11/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_11/</guid><pubDate>Wed, 20 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 6 - Fourier Transform</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081_6/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081_6/</guid><pubDate>Wed, 20 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 10 - General regions (1)</title><link>https://rezvan.xyz/chalmers/lma017/lma017_10/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_10/</guid><pubDate>Tue, 19 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 9 - Double and triple integrals</title><link>https://rezvan.xyz/chalmers/lma017/lma017_9/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_9/</guid><pubDate>Fri, 15 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 5 - Fourier series</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081_5/</guid><pubDate>Fri, 15 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 4 - Differential equation models</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081_4/</guid><pubDate>Thu, 14 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 8 - Lagrange multipliers</title><link>https://rezvan.xyz/chalmers/lma017/lma017_8/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_8/</guid><pubDate>Wed, 13 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 7 - Absolute max and min values</title><link>https://rezvan.xyz/chalmers/lma017/lma017_7/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_7/</guid><pubDate>Tue, 12 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 6 - Maximum and minimum values</title><link>https://rezvan.xyz/chalmers/lma017/lma017_6/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_6/</guid><pubDate>Fri, 08 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 5 - Directional derivatives</title><link>https://rezvan.xyz/chalmers/lma017/lma017_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_5/</guid><pubDate>Wed, 06 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 3 - Convolution</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081_3/</guid><pubDate>Tue, 05 Sep 2023 19:03:17 GMT</pubDate></item><item><title>Part 4 - Chain rule</title><link>https://rezvan.xyz/chalmers/lma017/lma017_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_4/</guid><pubDate>Tue, 05 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 2 - System properties &amp; LTI</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081_2/</guid><pubDate>Mon, 04 Sep 2023 20:03:17 GMT</pubDate></item><item><title>Part 3 - Higher partial derivatives</title><link>https://rezvan.xyz/chalmers/lma017/lma017_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_3/</guid><pubDate>Fri, 01 Sep 2023 08:53:01 GMT</pubDate></item><item><title>Part 2 - Continuity &amp; partial derivatives.</title><link>https://rezvan.xyz/chalmers/lma017/lma017_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_2/</guid><pubDate>Wed, 30 Aug 2023 08:53:01 GMT</pubDate></item><item><title>Part 1 - Signals</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081/</guid><pubDate>Tue, 29 Aug 2023 14:12:51 GMT</pubDate></item><item><title>Part 1 - Functions of several variables</title><link>https://rezvan.xyz/chalmers/lma017/lma017/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017/</guid><pubDate>Tue, 29 Aug 2023 08:53:01 GMT</pubDate></item><item><title>Part 9 - Summary</title><link>https://rezvan.xyz/chalmers/eda333/eda333_summary/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda333/eda333_summary/</guid><pubDate>Thu, 25 May 2023 09:22:18 GMT</pubDate></item><item><title>Part 14 - Summary</title><link>https://rezvan.xyz/chalmers/eem076/eem076_summary/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_summary/</guid><pubDate>Fri, 19 May 2023 14:57:46 GMT</pubDate></item><item><title>Part 13 - Op-Amps and Filters</title><link>https://rezvan.xyz/chalmers/eem076/eem076_13/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_13/</guid><pubDate>Fri, 19 May 2023 09:34:16 GMT</pubDate></item><item><title>Part 12 - Power in AC Circuits</title><link>https://rezvan.xyz/chalmers/eem076/eem076_12/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_12/</guid><pubDate>Fri, 12 May 2023 08:06:12 GMT</pubDate></item><item><title>Part 11 - Calculation methods for AC-circuits</title><link>https://rezvan.xyz/chalmers/eem076/eem076_11/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_11/</guid><pubDate>Mon, 08 May 2023 14:36:54 GMT</pubDate></item><item><title>Part 10 - Steady-state sinusoidal analysis</title><link>https://rezvan.xyz/chalmers/eem076/eem076_10/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_10/</guid><pubDate>Tue, 02 May 2023 13:33:02 GMT</pubDate></item><item><title>Part 8 - Parallel Processors</title><link>https://rezvan.xyz/chalmers/eda333/eda333_8/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda333/eda333_8/</guid><pubDate>Fri, 28 Apr 2023 16:12:01 GMT</pubDate></item><item><title>Part 9 - Electromagnetic Waves</title><link>https://rezvan.xyz/chalmers/eem076/eem076_9/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_9/</guid><pubDate>Tue, 25 Apr 2023 17:40:29 GMT</pubDate></item><item><title>Part 7 - Floating-point arithmetic</title><link>https://rezvan.xyz/chalmers/eda333/eda333_7/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda333/eda333_7/</guid><pubDate>Tue, 25 Apr 2023 13:18:21 GMT</pubDate></item><item><title>Part 8 - Magnetic fields</title><link>https://rezvan.xyz/chalmers/eem076/eem076_8/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_8/</guid><pubDate>Mon, 24 Apr 2023 15:33:32 GMT</pubDate></item><item><title>Part 6 - Virtual Memory</title><link>https://rezvan.xyz/chalmers/eda333/eda333_6/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda333/eda333_6/</guid><pubDate>Fri, 21 Apr 2023 17:28:25 GMT</pubDate></item><item><title>Part 7 - Electrical &amp; Magnetic fields</title><link>https://rezvan.xyz/chalmers/eem076/eem076_7/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_7/</guid><pubDate>Tue, 18 Apr 2023 14:54:06 GMT</pubDate></item><item><title>Part 6 - Work, Voltage and Capacitance</title><link>https://rezvan.xyz/chalmers/eem076/eem076_6/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_6/</guid><pubDate>Tue, 18 Apr 2023 10:05:29 GMT</pubDate></item><item><title>Part 5 - Cache memory</title><link>https://rezvan.xyz/chalmers/eda333/eda333_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda333/eda333_5/</guid><pubDate>Thu, 13 Apr 2023 18:04:58 GMT</pubDate></item><item><title>Part 4 - Pipeline hardware</title><link>https://rezvan.xyz/chalmers/eda333/eda333_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda333/eda333_4/</guid><pubDate>Tue, 28 Mar 2023 00:00:00 GMT</pubDate></item><item><title>Part 5 - Electrical fields</title><link>https://rezvan.xyz/chalmers/eem076/eem076_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_5/</guid><pubDate>Mon, 27 Mar 2023 16:20:46 GMT</pubDate></item><item><title>Part 3 - Pipelining</title><link>https://rezvan.xyz/chalmers/eda333/eda333_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda333/eda333_3/</guid><pubDate>Mon, 27 Mar 2023 00:00:00 GMT</pubDate></item><item><title>Part 4 - Capacitance and Inductance</title><link>https://rezvan.xyz/chalmers/eem076/eem076_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_4/</guid><pubDate>Sun, 26 Mar 2023 00:00:00 GMT</pubDate></item><item><title>Part 3 - Equivalent circuits</title><link>https://rezvan.xyz/chalmers/eem076/eem076_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_3/</guid><pubDate>Fri, 24 Mar 2023 00:00:00 GMT</pubDate></item><item><title>Part 2 - MIPS</title><link>https://rezvan.xyz/chalmers/eda333/eda333_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda333/eda333_2/</guid><pubDate>Wed, 22 Mar 2023 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction</title><link>https://rezvan.xyz/chalmers/eda333/eda333/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda333/eda333/</guid><pubDate>Tue, 21 Mar 2023 00:00:00 GMT</pubDate></item><item><title>Part 2 - Power &amp; Energy</title><link>https://rezvan.xyz/chalmers/eem076/eem076_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_2/</guid><pubDate>Tue, 21 Mar 2023 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction</title><link>https://rezvan.xyz/chalmers/eem076/eem076/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076/</guid><pubDate>Mon, 20 Mar 2023 00:00:00 GMT</pubDate></item><item><title>Part 9 - Testing</title><link>https://rezvan.xyz/chalmers/eda322/eda322_9/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda322/eda322_9/</guid><pubDate>Sun, 05 Mar 2023 00:00:00 GMT</pubDate></item><item><title>Part 8 - Interfaces and Memory</title><link>https://rezvan.xyz/chalmers/eda322/eda322_8/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda322/eda322_8/</guid><pubDate>Sun, 19 Feb 2023 00:00:00 GMT</pubDate></item><item><title>Part 10 - Parallel linked lists</title><link>https://rezvan.xyz/chalmers/tda384/tda384_10/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tda384/tda384_10/</guid><pubDate>Sun, 19 Feb 2023 00:00:00 GMT</pubDate></item><item><title>Part 9 - Parallelizing computations</title><link>https://rezvan.xyz/chalmers/tda384/tda384_9/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tda384/tda384_9/</guid><pubDate>Mon, 13 Feb 2023 00:00:00 GMT</pubDate></item><item><title>Part 7 - Timing, delay &amp; power</title><link>https://rezvan.xyz/chalmers/eda322/eda322_7/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda322/eda322_7/</guid><pubDate>Wed, 08 Feb 2023 00:00:00 GMT</pubDate></item><item><title>Part 8 - Synchronization problems (2)</title><link>https://rezvan.xyz/chalmers/tda384/tda384_8/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tda384/tda384_8/</guid><pubDate>Tue, 07 Feb 2023 13:05:43 GMT</pubDate></item><item><title>Part 6 - Reconfigurable Hardware</title><link>https://rezvan.xyz/chalmers/eda322/eda322_6/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda322/eda322_6/</guid><pubDate>Sun, 05 Feb 2023 14:28:10 GMT</pubDate></item><item><title>Part 6 &amp; 7 - Message-Passing Concurrency</title><link>https://rezvan.xyz/chalmers/tda384/tda384_6/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tda384/tda384_6/</guid><pubDate>Sat, 04 Feb 2023 00:00:00 GMT</pubDate></item><item><title>Part 5 - Monitors</title><link>https://rezvan.xyz/chalmers/tda384/tda384_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tda384/tda384_5/</guid><pubDate>Fri, 03 Feb 2023 17:16:30 GMT</pubDate></item><item><title>Part 5 - Arithmetic Units</title><link>https://rezvan.xyz/chalmers/eda322/eda322_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda322/eda322_5/</guid><pubDate>Fri, 03 Feb 2023 00:00:00 GMT</pubDate></item><item><title>Part 4 - Synchronization problems (1)</title><link>https://rezvan.xyz/chalmers/tda384/tda384_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tda384/tda384_4/</guid><pubDate>Wed, 01 Feb 2023 00:00:00 GMT</pubDate></item><item><title>Part 4 - Finite State Machines</title><link>https://rezvan.xyz/chalmers/eda322/eda322_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda322/eda322_4/</guid><pubDate>Tue, 31 Jan 2023 20:12:55 GMT</pubDate></item><item><title>Part 3 - Models of concurrency</title><link>https://rezvan.xyz/chalmers/tda384/tda384_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tda384/tda384_3/</guid><pubDate>Tue, 31 Jan 2023 00:00:00 GMT</pubDate></item><item><title>Part 3 - Sequential Circuits</title><link>https://rezvan.xyz/chalmers/eda322/eda322_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda322/eda322_3/</guid><pubDate>Tue, 24 Jan 2023 00:00:00 GMT</pubDate></item><item><title>Part 2 - Races, Locks, and Semaphores</title><link>https://rezvan.xyz/chalmers/tda384/tda384_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tda384/tda384_2/</guid><pubDate>Thu, 19 Jan 2023 00:00:00 GMT</pubDate></item><item><title>Part 2 - Binary Adders</title><link>https://rezvan.xyz/chalmers/eda322/eda322_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda322/eda322_2/</guid><pubDate>Wed, 18 Jan 2023 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction &amp; Boolean Algebra</title><link>https://rezvan.xyz/chalmers/eda322/eda322/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda322/eda322/</guid><pubDate>Mon, 16 Jan 2023 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction</title><link>https://rezvan.xyz/chalmers/tda384/tda384/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tda384/tda384/</guid><pubDate>Mon, 16 Jan 2023 00:00:00 GMT</pubDate></item><item><title>Programming Principles</title><link>https://rezvan.xyz/posts/programming_principles/</link><guid isPermaLink="true">https://rezvan.xyz/posts/programming_principles/</guid><pubDate>Mon, 09 Jan 2023 16:03:59 GMT</pubDate></item><item><title>Part 10 - Complexity (2)</title><link>https://rezvan.xyz/chalmers/dat038/dat038_10/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038_10/</guid><pubDate>Fri, 09 Dec 2022 17:49:03 GMT</pubDate></item><item><title>Part 9 - Shortest Path &amp; Spanning Trees</title><link>https://rezvan.xyz/chalmers/dat038/dat038_9/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038_9/</guid><pubDate>Wed, 07 Dec 2022 17:34:09 GMT</pubDate></item><item><title>Part 2 - Light waves</title><link>https://rezvan.xyz/chalmers/tif085/tif085_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tif085/tif085_5/</guid><pubDate>Wed, 07 Dec 2022 16:55:57 GMT</pubDate></item><item><title>Part 8 - Graphs</title><link>https://rezvan.xyz/chalmers/dat038/dat038_8/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038_8/</guid><pubDate>Tue, 06 Dec 2022 12:08:43 GMT</pubDate></item><item><title>Part 7 - Binary Heaps</title><link>https://rezvan.xyz/chalmers/dat038/dat038_7/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038_7/</guid><pubDate>Sun, 04 Dec 2022 17:18:49 GMT</pubDate></item><item><title>Part 1 - Mechanical Waves</title><link>https://rezvan.xyz/chalmers/tif085/tif085_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tif085/tif085_4/</guid><pubDate>Sun, 04 Dec 2022 16:23:27 GMT</pubDate></item><item><title>Part 6 - Trees</title><link>https://rezvan.xyz/chalmers/dat038/dat038_6/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038_6/</guid><pubDate>Wed, 30 Nov 2022 17:08:48 GMT</pubDate></item><item><title>Part 5 - Hash Tables</title><link>https://rezvan.xyz/chalmers/dat038/dat038_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038_5/</guid><pubDate>Tue, 29 Nov 2022 17:50:23 GMT</pubDate></item><item><title>Part 4 - Abstract Data Types</title><link>https://rezvan.xyz/chalmers/dat038/dat038_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038_4/</guid><pubDate>Mon, 28 Nov 2022 19:30:47 GMT</pubDate></item><item><title>Lecture 3</title><link>https://rezvan.xyz/chalmers/tif085/tif085_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tif085/tif085_3/</guid><pubDate>Mon, 28 Nov 2022 17:14:58 GMT</pubDate></item><item><title>Part 3 - Dynamic Arrays</title><link>https://rezvan.xyz/chalmers/dat038/dat038_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038_3/</guid><pubDate>Sun, 27 Nov 2022 16:26:09 GMT</pubDate></item><item><title>Lecture 2</title><link>https://rezvan.xyz/chalmers/tif085/tif085_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tif085/tif085_2/</guid><pubDate>Fri, 25 Nov 2022 23:04:21 GMT</pubDate></item><item><title>Part 2 - Complexity (1)</title><link>https://rezvan.xyz/chalmers/dat038/dat038_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038_2/</guid><pubDate>Fri, 25 Nov 2022 16:20:46 GMT</pubDate></item><item><title>Part 1 - Sorting</title><link>https://rezvan.xyz/chalmers/dat038/dat038/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038/</guid><pubDate>Thu, 24 Nov 2022 18:57:27 GMT</pubDate></item><item><title>Lecture 1</title><link>https://rezvan.xyz/chalmers/tif085/tif085/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tif085/tif085/</guid><pubDate>Thu, 24 Nov 2022 16:57:38 GMT</pubDate></item><item><title>Julia projects</title><link>https://rezvan.xyz/posts/julia/</link><guid isPermaLink="true">https://rezvan.xyz/posts/julia/</guid><pubDate>Tue, 23 Aug 2022 19:00:47 GMT</pubDate></item><item><title>Vim-like editor</title><link>https://rezvan.xyz/posts/editor/</link><guid isPermaLink="true">https://rezvan.xyz/posts/editor/</guid><pubDate>Wed, 10 Aug 2022 19:04:50 GMT</pubDate></item><item><title>My personal bucket list</title><link>https://rezvan.xyz/posts/bucketlist/</link><guid isPermaLink="true">https://rezvan.xyz/posts/bucketlist/</guid><pubDate>Sun, 31 Jul 2022 15:21:34 GMT</pubDate></item><item><title>Initial post</title><link>https://rezvan.xyz/posts/initialpost/</link><guid isPermaLink="true">https://rezvan.xyz/posts/initialpost/</guid><pubDate>Fri, 29 Jul 2022 15:18:30 GMT</pubDate></item></channel></rss>
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+<?xml version="1.0" encoding="UTF-8"?><rss version="2.0"><channel><title>rezarezvan.com</title><description/><link>https://rezvan.xyz/</link><item><title>Uncertainty makes the soul</title><link>https://rezvan.xyz/posts/uncertainty/</link><guid isPermaLink="true">https://rezvan.xyz/posts/uncertainty/</guid><pubDate>Tue, 03 Dec 2024 00:00:00 GMT</pubDate></item><item><title>Part 9 - Discrete Systems</title><link>https://rezvan.xyz/cityu/bme3105/bme3105_9/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/bme3105/bme3105_9/</guid><pubDate>Fri, 22 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 5 - Multiple Linear Regression</title><link>https://rezvan.xyz/cityu/ma3518/ma3518_5/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/ma3518/ma3518_5/</guid><pubDate>Thu, 21 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 11 - High-Level and Low-Level Vision Applications</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_11/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_11/</guid><pubDate>Wed, 20 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 8 - Stability and Controller Design</title><link>https://rezvan.xyz/cityu/bme3105/bme3105_8/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/bme3105/bme3105_8/</guid><pubDate>Fri, 15 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 10 - Neural Networks and Deep Learning Part 2</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_10/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_10/</guid><pubDate>Wed, 13 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 10 - Future trends of Big Data</title><link>https://rezvan.xyz/cityu/is2021/is2021_10/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021_10/</guid><pubDate>Tue, 12 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 7 - State Space Realization</title><link>https://rezvan.xyz/cityu/bme3105/bme3105_7/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/bme3105/bme3105_7/</guid><pubDate>Fri, 08 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 4 - Simple Linear Regression</title><link>https://rezvan.xyz/cityu/ma3518/ma3518_4/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/ma3518/ma3518_4/</guid><pubDate>Thu, 07 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 9 - Neural Networks and Deep Learning</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_9/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_9/</guid><pubDate>Wed, 06 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 9 - NoSQL Data Management for Big Data</title><link>https://rezvan.xyz/cityu/is2021/is2021_9/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021_9/</guid><pubDate>Tue, 05 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 6 - State Space Approach</title><link>https://rezvan.xyz/cityu/bme3105/bme3105_6/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/bme3105/bme3105_6/</guid><pubDate>Fri, 01 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 7 - Thermal Actuators and Piezoresistivity</title><link>https://rezvan.xyz/cityu/mne3115/mne3115_7/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/mne3115/mne3115_7/</guid><pubDate>Fri, 01 Nov 2024 00:00:00 GMT</pubDate></item><item><title>Part 8 - Principal Component Analysis</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_8/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_8/</guid><pubDate>Wed, 30 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 8 - Data Governance for BDA – Data Policies &amp; Processes</title><link>https://rezvan.xyz/cityu/is2021/is2021_8/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021_8/</guid><pubDate>Tue, 29 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 5 - Stability</title><link>https://rezvan.xyz/cityu/bme3105/bme3105_5/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/bme3105/bme3105_5/</guid><pubDate>Fri, 25 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 7 - The Expectation Maximization Algorithm &amp; Linear Dimensionality Reduction</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_7/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_7/</guid><pubDate>Wed, 23 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 6 - Elasticity</title><link>https://rezvan.xyz/cityu/mne3115/mne3115_6/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/mne3115/mne3115_6/</guid><pubDate>Fri, 18 Oct 2024 23:15:00 GMT</pubDate></item><item><title>Part 5 - Fabrication Techniques</title><link>https://rezvan.xyz/cityu/mne3115/mne3115_5/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/mne3115/mne3115_5/</guid><pubDate>Fri, 18 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 6 - Robust, Non-Linear Regression and Clustering</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_6/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_6/</guid><pubDate>Wed, 16 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 7 - Developing a Strategy for Integrating Big Data Analytics into the Enterprise</title><link>https://rezvan.xyz/cityu/is2021/is2021_7/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021_7/</guid><pubDate>Tue, 15 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 5 - Regression</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_5/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_5/</guid><pubDate>Wed, 09 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Never put your life on hold</title><link>https://rezvan.xyz/posts/pause/</link><guid isPermaLink="true">https://rezvan.xyz/posts/pause/</guid><pubDate>Fri, 04 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 4 - Time Respone</title><link>https://rezvan.xyz/cityu/bme3105/bme3105_4/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/bme3105/bme3105_4/</guid><pubDate>Fri, 04 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 4 - Etching</title><link>https://rezvan.xyz/cityu/mne3115/mne3115_4/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/mne3115/mne3115_4/</guid><pubDate>Fri, 04 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 4 - Duality and SVM</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_4/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_4/</guid><pubDate>Wed, 02 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 6 - Achieving Organizational Alignment for Big Data Analytics</title><link>https://rezvan.xyz/cityu/is2021/is2021_6/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021_6/</guid><pubDate>Tue, 01 Oct 2024 00:00:00 GMT</pubDate></item><item><title>Part 3 - Modelling in Frequency Domain</title><link>https://rezvan.xyz/cityu/bme3105/bme3105_3/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/bme3105/bme3105_3/</guid><pubDate>Fri, 27 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 3 - Thin Film Growth and Deposition</title><link>https://rezvan.xyz/cityu/mne3115/mne3115_3/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/mne3115/mne3115_3/</guid><pubDate>Fri, 27 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 3 - Optimization and Convexity</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_3/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_3/</guid><pubDate>Wed, 25 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 5 - Developing Big Data Applications</title><link>https://rezvan.xyz/cityu/is2021/is2021_5/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021_5/</guid><pubDate>Tue, 24 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 4 - Big Data Tools and Techniques</title><link>https://rezvan.xyz/cityu/is2021/is2021_4/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021_4/</guid><pubDate>Sat, 21 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 2 - Photolithography</title><link>https://rezvan.xyz/cityu/mne3115/mne3115_2/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/mne3115/mne3115_2/</guid><pubDate>Fri, 20 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 3 - Confidence Interval and Hypothesis Testing</title><link>https://rezvan.xyz/cityu/ma3518/ma3518_3/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/ma3518/ma3518_3/</guid><pubDate>Thu, 19 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 3 - High-Performance Applications</title><link>https://rezvan.xyz/cityu/is2021/is2021_3/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021_3/</guid><pubDate>Tue, 17 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 2 - System Modelling</title><link>https://rezvan.xyz/cityu/bme3105/bme3105_2/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/bme3105/bme3105_2/</guid><pubDate>Fri, 13 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 2 - Basic Statistical Concepts and Tools</title><link>https://rezvan.xyz/cityu/ma3518/ma3518_2/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/ma3518/ma3518_2/</guid><pubDate>Thu, 12 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 2 - Generative VS. Discriminative Models</title><link>https://rezvan.xyz/cityu/cs4487/cs4487_2/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487_2/</guid><pubDate>Wed, 11 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 2 - Business Drivers for Big Data Analytics &amp; its related Business Problems</title><link>https://rezvan.xyz/cityu/is2021/is2021_2/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021_2/</guid><pubDate>Tue, 10 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction</title><link>https://rezvan.xyz/cityu/bme3105/bme3105/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/bme3105/bme3105/</guid><pubDate>Fri, 06 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction</title><link>https://rezvan.xyz/cityu/mne3115/mne3115/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/mne3115/mne3115/</guid><pubDate>Fri, 06 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction to R</title><link>https://rezvan.xyz/cityu/ma3518/ma3518/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/ma3518/ma3518/</guid><pubDate>Thu, 05 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction</title><link>https://rezvan.xyz/cityu/cs4487/cs4487/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/cs4487/cs4487/</guid><pubDate>Wed, 04 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Part 1 - Evolution of Data Management</title><link>https://rezvan.xyz/cityu/is2021/is2021/</link><guid isPermaLink="true">https://rezvan.xyz/cityu/is2021/is2021/</guid><pubDate>Tue, 03 Sep 2024 00:00:00 GMT</pubDate></item><item><title>Links</title><link>https://rezvan.xyz/posts/links/</link><guid isPermaLink="true">https://rezvan.xyz/posts/links/</guid><pubDate>Wed, 17 Jul 2024 00:00:00 GMT</pubDate></item><item><title>Part 9 - Machine Learning</title><link>https://rezvan.xyz/chalmers/dat565/dat565_9/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat565/dat565_9/</guid><pubDate>Tue, 20 Feb 2024 00:00:00 GMT</pubDate></item><item><title>Part 8 - Distance and network methods</title><link>https://rezvan.xyz/chalmers/dat565/dat565_8/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat565/dat565_8/</guid><pubDate>Tue, 13 Feb 2024 00:00:00 GMT</pubDate></item><item><title>Part 7 - Linear and logistic regression</title><link>https://rezvan.xyz/chalmers/dat565/dat565_7/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat565/dat565_7/</guid><pubDate>Tue, 06 Feb 2024 00:00:00 GMT</pubDate></item><item><title>Part 6 - Mathematical models</title><link>https://rezvan.xyz/chalmers/dat565/dat565_6/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat565/dat565_6/</guid><pubDate>Fri, 02 Feb 2024 00:00:00 GMT</pubDate></item><item><title>Part 5 - Statistical analysis</title><link>https://rezvan.xyz/chalmers/dat565/dat565_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat565/dat565_5/</guid><pubDate>Sat, 27 Jan 2024 00:00:00 GMT</pubDate></item><item><title>Part 4 - Data visualization</title><link>https://rezvan.xyz/chalmers/dat565/dat565_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat565/dat565_4/</guid><pubDate>Fri, 26 Jan 2024 00:00:00 GMT</pubDate></item><item><title>Part 3 - Data munging</title><link>https://rezvan.xyz/chalmers/dat565/dat565_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat565/dat565_3/</guid><pubDate>Tue, 23 Jan 2024 00:00:00 GMT</pubDate></item><item><title>Part 2 - Python tools for data science</title><link>https://rezvan.xyz/chalmers/dat565/dat565_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat565/dat565_2/</guid><pubDate>Fri, 19 Jan 2024 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction</title><link>https://rezvan.xyz/chalmers/dat565/dat565/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat565/dat565/</guid><pubDate>Tue, 16 Jan 2024 00:00:00 GMT</pubDate></item><item><title>Part 15 - Summary</title><link>https://rezvan.xyz/chalmers/ere103/ere103_summary/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_summary/</guid><pubDate>Sat, 30 Dec 2023 00:00:00 GMT</pubDate></item><item><title>Part 14 - Filters</title><link>https://rezvan.xyz/chalmers/ere103/ere103_14/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_14/</guid><pubDate>Thu, 07 Dec 2023 00:00:00 GMT</pubDate></item><item><title>Part 13 - Discretization</title><link>https://rezvan.xyz/chalmers/ere103/ere103_13/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_13/</guid><pubDate>Wed, 06 Dec 2023 00:00:00 GMT</pubDate></item><item><title>Part 12 - State feedback</title><link>https://rezvan.xyz/chalmers/ere103/ere103_12/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_12/</guid><pubDate>Tue, 05 Dec 2023 00:00:00 GMT</pubDate></item><item><title>Part 11 - Design of controllers (2)</title><link>https://rezvan.xyz/chalmers/ere103/ere103_11/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_11/</guid><pubDate>Tue, 28 Nov 2023 00:00:00 GMT</pubDate></item><item><title>Part 10 - Design of controllers</title><link>https://rezvan.xyz/chalmers/ere103/ere103_10/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_10/</guid><pubDate>Mon, 27 Nov 2023 00:00:00 GMT</pubDate></item><item><title>Part 9 - General controller structure</title><link>https://rezvan.xyz/chalmers/ere103/ere103_9/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_9/</guid><pubDate>Thu, 23 Nov 2023 00:00:00 GMT</pubDate></item><item><title>Part 8 - Stability</title><link>https://rezvan.xyz/chalmers/ere103/ere103_8/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_8/</guid><pubDate>Thu, 16 Nov 2023 00:00:00 GMT</pubDate></item><item><title>Part 7 - Bode plot</title><link>https://rezvan.xyz/chalmers/ere103/ere103_7/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_7/</guid><pubDate>Mon, 13 Nov 2023 00:00:00 GMT</pubDate></item><item><title>Part 6 - Space-state representation (2)</title><link>https://rezvan.xyz/chalmers/ere103/ere103_6/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_6/</guid><pubDate>Thu, 09 Nov 2023 00:00:00 GMT</pubDate></item><item><title>Part 5 - Space-state representation (1)</title><link>https://rezvan.xyz/chalmers/ere103/ere103_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_5/</guid><pubDate>Tue, 07 Nov 2023 00:00:00 GMT</pubDate></item><item><title>Part 4 - Models for mechanical systems</title><link>https://rezvan.xyz/chalmers/ere103/ere103_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_4/</guid><pubDate>Mon, 06 Nov 2023 00:00:00 GMT</pubDate></item><item><title>Part 3 - Controllers in the Laplace domain</title><link>https://rezvan.xyz/chalmers/ere103/ere103_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_3/</guid><pubDate>Sun, 05 Nov 2023 00:00:00 GMT</pubDate></item><item><title>Part 2 - Transfer functions</title><link>https://rezvan.xyz/chalmers/ere103/ere103_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103_2/</guid><pubDate>Tue, 31 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction</title><link>https://rezvan.xyz/chalmers/ere103/ere103/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ere103/ere103/</guid><pubDate>Mon, 30 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 21 - Summary</title><link>https://rezvan.xyz/chalmers/lma017/lma017_summary/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_summary/</guid><pubDate>Thu, 19 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 20 - Divergence and Stokes&apos; Theorem</title><link>https://rezvan.xyz/chalmers/lma017/lma017_20/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_20/</guid><pubDate>Wed, 18 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 10 - Summary</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081_summary/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081_summary/</guid><pubDate>Sun, 15 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 19 - Surface integrals</title><link>https://rezvan.xyz/chalmers/lma017/lma017_19/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_19/</guid><pubDate>Wed, 11 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 18 - Green&apos;s Theorem</title><link>https://rezvan.xyz/chalmers/lma017/lma017_18/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_18/</guid><pubDate>Tue, 10 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 17 - Gradient theorem</title><link>https://rezvan.xyz/chalmers/lma017/lma017_17/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_17/</guid><pubDate>Wed, 04 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 16 - Vector fields</title><link>https://rezvan.xyz/chalmers/lma017/lma017_16/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_16/</guid><pubDate>Tue, 03 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 15 - Line integrals</title><link>https://rezvan.xyz/chalmers/lma017/lma017_15/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_15/</guid><pubDate>Sun, 01 Oct 2023 00:00:00 GMT</pubDate></item><item><title>Part 9 - Laplace transform</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081_9/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081_9/</guid><pubDate>Thu, 28 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 14 - Curves</title><link>https://rezvan.xyz/chalmers/lma017/lma017_14/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_14/</guid><pubDate>Wed, 27 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 13 - The Jacobian</title><link>https://rezvan.xyz/chalmers/lma017/lma017_13/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_13/</guid><pubDate>Tue, 26 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 8 - Signal reconstruction</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081_8/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081_8/</guid><pubDate>Mon, 25 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 12 - Change of variables</title><link>https://rezvan.xyz/chalmers/lma017/lma017_12/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_12/</guid><pubDate>Fri, 22 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 7 - Nyquist-Shannon sampling theorem</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081_7/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081_7/</guid><pubDate>Thu, 21 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 11 - General regions (2)</title><link>https://rezvan.xyz/chalmers/lma017/lma017_11/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_11/</guid><pubDate>Wed, 20 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 6 - Fourier Transform</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081_6/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081_6/</guid><pubDate>Wed, 20 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 10 - General regions (1)</title><link>https://rezvan.xyz/chalmers/lma017/lma017_10/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_10/</guid><pubDate>Tue, 19 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 9 - Double and triple integrals</title><link>https://rezvan.xyz/chalmers/lma017/lma017_9/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_9/</guid><pubDate>Fri, 15 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 5 - Fourier series</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081_5/</guid><pubDate>Fri, 15 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 4 - Differential equation models</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081_4/</guid><pubDate>Thu, 14 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 8 - Lagrange multipliers</title><link>https://rezvan.xyz/chalmers/lma017/lma017_8/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_8/</guid><pubDate>Wed, 13 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 7 - Absolute max and min values</title><link>https://rezvan.xyz/chalmers/lma017/lma017_7/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_7/</guid><pubDate>Tue, 12 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 6 - Maximum and minimum values</title><link>https://rezvan.xyz/chalmers/lma017/lma017_6/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_6/</guid><pubDate>Fri, 08 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 5 - Directional derivatives</title><link>https://rezvan.xyz/chalmers/lma017/lma017_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_5/</guid><pubDate>Wed, 06 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 3 - Convolution</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081_3/</guid><pubDate>Tue, 05 Sep 2023 19:03:17 GMT</pubDate></item><item><title>Part 4 - Chain rule</title><link>https://rezvan.xyz/chalmers/lma017/lma017_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_4/</guid><pubDate>Tue, 05 Sep 2023 00:00:00 GMT</pubDate></item><item><title>Part 2 - System properties &amp; LTI</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081_2/</guid><pubDate>Mon, 04 Sep 2023 20:03:17 GMT</pubDate></item><item><title>Part 3 - Higher partial derivatives</title><link>https://rezvan.xyz/chalmers/lma017/lma017_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_3/</guid><pubDate>Fri, 01 Sep 2023 08:53:01 GMT</pubDate></item><item><title>Part 2 - Continuity &amp; partial derivatives.</title><link>https://rezvan.xyz/chalmers/lma017/lma017_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017_2/</guid><pubDate>Wed, 30 Aug 2023 08:53:01 GMT</pubDate></item><item><title>Part 1 - Signals</title><link>https://rezvan.xyz/chalmers/ssy081/ssy081/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/ssy081/ssy081/</guid><pubDate>Tue, 29 Aug 2023 14:12:51 GMT</pubDate></item><item><title>Part 1 - Functions of several variables</title><link>https://rezvan.xyz/chalmers/lma017/lma017/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/lma017/lma017/</guid><pubDate>Tue, 29 Aug 2023 08:53:01 GMT</pubDate></item><item><title>Part 9 - Summary</title><link>https://rezvan.xyz/chalmers/eda333/eda333_summary/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda333/eda333_summary/</guid><pubDate>Thu, 25 May 2023 09:22:18 GMT</pubDate></item><item><title>Part 14 - Summary</title><link>https://rezvan.xyz/chalmers/eem076/eem076_summary/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_summary/</guid><pubDate>Fri, 19 May 2023 14:57:46 GMT</pubDate></item><item><title>Part 13 - Op-Amps and Filters</title><link>https://rezvan.xyz/chalmers/eem076/eem076_13/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_13/</guid><pubDate>Fri, 19 May 2023 09:34:16 GMT</pubDate></item><item><title>Part 12 - Power in AC Circuits</title><link>https://rezvan.xyz/chalmers/eem076/eem076_12/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_12/</guid><pubDate>Fri, 12 May 2023 08:06:12 GMT</pubDate></item><item><title>Part 11 - Calculation methods for AC-circuits</title><link>https://rezvan.xyz/chalmers/eem076/eem076_11/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_11/</guid><pubDate>Mon, 08 May 2023 14:36:54 GMT</pubDate></item><item><title>Part 10 - Steady-state sinusoidal analysis</title><link>https://rezvan.xyz/chalmers/eem076/eem076_10/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_10/</guid><pubDate>Tue, 02 May 2023 13:33:02 GMT</pubDate></item><item><title>Part 8 - Parallel Processors</title><link>https://rezvan.xyz/chalmers/eda333/eda333_8/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda333/eda333_8/</guid><pubDate>Fri, 28 Apr 2023 16:12:01 GMT</pubDate></item><item><title>Part 9 - Electromagnetic Waves</title><link>https://rezvan.xyz/chalmers/eem076/eem076_9/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_9/</guid><pubDate>Tue, 25 Apr 2023 17:40:29 GMT</pubDate></item><item><title>Part 7 - Floating-point arithmetic</title><link>https://rezvan.xyz/chalmers/eda333/eda333_7/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda333/eda333_7/</guid><pubDate>Tue, 25 Apr 2023 13:18:21 GMT</pubDate></item><item><title>Part 8 - Magnetic fields</title><link>https://rezvan.xyz/chalmers/eem076/eem076_8/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_8/</guid><pubDate>Mon, 24 Apr 2023 15:33:32 GMT</pubDate></item><item><title>Part 6 - Virtual Memory</title><link>https://rezvan.xyz/chalmers/eda333/eda333_6/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda333/eda333_6/</guid><pubDate>Fri, 21 Apr 2023 17:28:25 GMT</pubDate></item><item><title>Part 7 - Electrical &amp; Magnetic fields</title><link>https://rezvan.xyz/chalmers/eem076/eem076_7/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_7/</guid><pubDate>Tue, 18 Apr 2023 14:54:06 GMT</pubDate></item><item><title>Part 6 - Work, Voltage and Capacitance</title><link>https://rezvan.xyz/chalmers/eem076/eem076_6/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_6/</guid><pubDate>Tue, 18 Apr 2023 10:05:29 GMT</pubDate></item><item><title>Part 5 - Cache memory</title><link>https://rezvan.xyz/chalmers/eda333/eda333_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda333/eda333_5/</guid><pubDate>Thu, 13 Apr 2023 18:04:58 GMT</pubDate></item><item><title>Part 4 - Pipeline hardware</title><link>https://rezvan.xyz/chalmers/eda333/eda333_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda333/eda333_4/</guid><pubDate>Tue, 28 Mar 2023 00:00:00 GMT</pubDate></item><item><title>Part 5 - Electrical fields</title><link>https://rezvan.xyz/chalmers/eem076/eem076_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_5/</guid><pubDate>Mon, 27 Mar 2023 16:20:46 GMT</pubDate></item><item><title>Part 3 - Pipelining</title><link>https://rezvan.xyz/chalmers/eda333/eda333_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda333/eda333_3/</guid><pubDate>Mon, 27 Mar 2023 00:00:00 GMT</pubDate></item><item><title>Part 4 - Capacitance and Inductance</title><link>https://rezvan.xyz/chalmers/eem076/eem076_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_4/</guid><pubDate>Sun, 26 Mar 2023 00:00:00 GMT</pubDate></item><item><title>Part 3 - Equivalent circuits</title><link>https://rezvan.xyz/chalmers/eem076/eem076_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_3/</guid><pubDate>Fri, 24 Mar 2023 00:00:00 GMT</pubDate></item><item><title>Part 2 - MIPS</title><link>https://rezvan.xyz/chalmers/eda333/eda333_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda333/eda333_2/</guid><pubDate>Wed, 22 Mar 2023 00:00:00 GMT</pubDate></item><item><title>Part 2 - Power &amp; Energy</title><link>https://rezvan.xyz/chalmers/eem076/eem076_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076_2/</guid><pubDate>Tue, 21 Mar 2023 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction</title><link>https://rezvan.xyz/chalmers/eda333/eda333/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda333/eda333/</guid><pubDate>Tue, 21 Mar 2023 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction</title><link>https://rezvan.xyz/chalmers/eem076/eem076/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eem076/eem076/</guid><pubDate>Mon, 20 Mar 2023 00:00:00 GMT</pubDate></item><item><title>Part 9 - Testing</title><link>https://rezvan.xyz/chalmers/eda322/eda322_9/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda322/eda322_9/</guid><pubDate>Sun, 05 Mar 2023 00:00:00 GMT</pubDate></item><item><title>Part 8 - Interfaces and Memory</title><link>https://rezvan.xyz/chalmers/eda322/eda322_8/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda322/eda322_8/</guid><pubDate>Sun, 19 Feb 2023 00:00:00 GMT</pubDate></item><item><title>Part 10 - Parallel linked lists</title><link>https://rezvan.xyz/chalmers/tda384/tda384_10/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tda384/tda384_10/</guid><pubDate>Sun, 19 Feb 2023 00:00:00 GMT</pubDate></item><item><title>Part 9 - Parallelizing computations</title><link>https://rezvan.xyz/chalmers/tda384/tda384_9/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tda384/tda384_9/</guid><pubDate>Mon, 13 Feb 2023 00:00:00 GMT</pubDate></item><item><title>Part 7 - Timing, delay &amp; power</title><link>https://rezvan.xyz/chalmers/eda322/eda322_7/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda322/eda322_7/</guid><pubDate>Wed, 08 Feb 2023 00:00:00 GMT</pubDate></item><item><title>Part 8 - Synchronization problems (2)</title><link>https://rezvan.xyz/chalmers/tda384/tda384_8/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tda384/tda384_8/</guid><pubDate>Tue, 07 Feb 2023 13:05:43 GMT</pubDate></item><item><title>Part 6 - Reconfigurable Hardware</title><link>https://rezvan.xyz/chalmers/eda322/eda322_6/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda322/eda322_6/</guid><pubDate>Sun, 05 Feb 2023 14:28:10 GMT</pubDate></item><item><title>Part 6 &amp; 7 - Message-Passing Concurrency</title><link>https://rezvan.xyz/chalmers/tda384/tda384_6/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tda384/tda384_6/</guid><pubDate>Sat, 04 Feb 2023 00:00:00 GMT</pubDate></item><item><title>Part 5 - Monitors</title><link>https://rezvan.xyz/chalmers/tda384/tda384_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tda384/tda384_5/</guid><pubDate>Fri, 03 Feb 2023 17:16:30 GMT</pubDate></item><item><title>Part 5 - Arithmetic Units</title><link>https://rezvan.xyz/chalmers/eda322/eda322_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda322/eda322_5/</guid><pubDate>Fri, 03 Feb 2023 00:00:00 GMT</pubDate></item><item><title>Part 4 - Synchronization problems (1)</title><link>https://rezvan.xyz/chalmers/tda384/tda384_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tda384/tda384_4/</guid><pubDate>Wed, 01 Feb 2023 00:00:00 GMT</pubDate></item><item><title>Part 4 - Finite State Machines</title><link>https://rezvan.xyz/chalmers/eda322/eda322_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda322/eda322_4/</guid><pubDate>Tue, 31 Jan 2023 20:12:55 GMT</pubDate></item><item><title>Part 3 - Models of concurrency</title><link>https://rezvan.xyz/chalmers/tda384/tda384_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tda384/tda384_3/</guid><pubDate>Tue, 31 Jan 2023 00:00:00 GMT</pubDate></item><item><title>Part 3 - Sequential Circuits</title><link>https://rezvan.xyz/chalmers/eda322/eda322_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda322/eda322_3/</guid><pubDate>Tue, 24 Jan 2023 00:00:00 GMT</pubDate></item><item><title>Part 2 - Races, Locks, and Semaphores</title><link>https://rezvan.xyz/chalmers/tda384/tda384_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tda384/tda384_2/</guid><pubDate>Thu, 19 Jan 2023 00:00:00 GMT</pubDate></item><item><title>Part 2 - Binary Adders</title><link>https://rezvan.xyz/chalmers/eda322/eda322_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda322/eda322_2/</guid><pubDate>Wed, 18 Jan 2023 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction &amp; Boolean Algebra</title><link>https://rezvan.xyz/chalmers/eda322/eda322/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/eda322/eda322/</guid><pubDate>Mon, 16 Jan 2023 00:00:00 GMT</pubDate></item><item><title>Part 1 - Introduction</title><link>https://rezvan.xyz/chalmers/tda384/tda384/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tda384/tda384/</guid><pubDate>Mon, 16 Jan 2023 00:00:00 GMT</pubDate></item><item><title>Programming Principles</title><link>https://rezvan.xyz/posts/programming_principles/</link><guid isPermaLink="true">https://rezvan.xyz/posts/programming_principles/</guid><pubDate>Mon, 09 Jan 2023 16:03:59 GMT</pubDate></item><item><title>Part 10 - Complexity (2)</title><link>https://rezvan.xyz/chalmers/dat038/dat038_10/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038_10/</guid><pubDate>Fri, 09 Dec 2022 17:49:03 GMT</pubDate></item><item><title>Part 9 - Shortest Path &amp; Spanning Trees</title><link>https://rezvan.xyz/chalmers/dat038/dat038_9/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038_9/</guid><pubDate>Wed, 07 Dec 2022 17:34:09 GMT</pubDate></item><item><title>Part 2 - Light waves</title><link>https://rezvan.xyz/chalmers/tif085/tif085_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tif085/tif085_5/</guid><pubDate>Wed, 07 Dec 2022 16:55:57 GMT</pubDate></item><item><title>Part 8 - Graphs</title><link>https://rezvan.xyz/chalmers/dat038/dat038_8/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038_8/</guid><pubDate>Tue, 06 Dec 2022 12:08:43 GMT</pubDate></item><item><title>Part 7 - Binary Heaps</title><link>https://rezvan.xyz/chalmers/dat038/dat038_7/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038_7/</guid><pubDate>Sun, 04 Dec 2022 17:18:49 GMT</pubDate></item><item><title>Part 1 - Mechanical Waves</title><link>https://rezvan.xyz/chalmers/tif085/tif085_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tif085/tif085_4/</guid><pubDate>Sun, 04 Dec 2022 16:23:27 GMT</pubDate></item><item><title>Part 6 - Trees</title><link>https://rezvan.xyz/chalmers/dat038/dat038_6/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038_6/</guid><pubDate>Wed, 30 Nov 2022 17:08:48 GMT</pubDate></item><item><title>Part 5 - Hash Tables</title><link>https://rezvan.xyz/chalmers/dat038/dat038_5/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038_5/</guid><pubDate>Tue, 29 Nov 2022 17:50:23 GMT</pubDate></item><item><title>Part 4 - Abstract Data Types</title><link>https://rezvan.xyz/chalmers/dat038/dat038_4/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038_4/</guid><pubDate>Mon, 28 Nov 2022 19:30:47 GMT</pubDate></item><item><title>Lecture 3</title><link>https://rezvan.xyz/chalmers/tif085/tif085_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tif085/tif085_3/</guid><pubDate>Mon, 28 Nov 2022 17:14:58 GMT</pubDate></item><item><title>Part 3 - Dynamic Arrays</title><link>https://rezvan.xyz/chalmers/dat038/dat038_3/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038_3/</guid><pubDate>Sun, 27 Nov 2022 16:26:09 GMT</pubDate></item><item><title>Lecture 2</title><link>https://rezvan.xyz/chalmers/tif085/tif085_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tif085/tif085_2/</guid><pubDate>Fri, 25 Nov 2022 23:04:21 GMT</pubDate></item><item><title>Part 2 - Complexity (1)</title><link>https://rezvan.xyz/chalmers/dat038/dat038_2/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038_2/</guid><pubDate>Fri, 25 Nov 2022 16:20:46 GMT</pubDate></item><item><title>Part 1 - Sorting</title><link>https://rezvan.xyz/chalmers/dat038/dat038/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/dat038/dat038/</guid><pubDate>Thu, 24 Nov 2022 18:57:27 GMT</pubDate></item><item><title>Lecture 1</title><link>https://rezvan.xyz/chalmers/tif085/tif085/</link><guid isPermaLink="true">https://rezvan.xyz/chalmers/tif085/tif085/</guid><pubDate>Thu, 24 Nov 2022 16:57:38 GMT</pubDate></item><item><title>Julia projects</title><link>https://rezvan.xyz/posts/julia/</link><guid isPermaLink="true">https://rezvan.xyz/posts/julia/</guid><pubDate>Tue, 23 Aug 2022 19:00:47 GMT</pubDate></item><item><title>Vim-like editor</title><link>https://rezvan.xyz/posts/editor/</link><guid isPermaLink="true">https://rezvan.xyz/posts/editor/</guid><pubDate>Wed, 10 Aug 2022 19:04:50 GMT</pubDate></item><item><title>My personal bucket list</title><link>https://rezvan.xyz/posts/bucketlist/</link><guid isPermaLink="true">https://rezvan.xyz/posts/bucketlist/</guid><pubDate>Sun, 31 Jul 2022 15:21:34 GMT</pubDate></item><item><title>Initial post</title><link>https://rezvan.xyz/posts/initialpost/</link><guid isPermaLink="true">https://rezvan.xyz/posts/initialpost/</guid><pubDate>Fri, 29 Jul 2022 15:18:30 GMT</pubDate></item></channel></rss>
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