From 245a697613467617e08eb9c03a8bd85483ff3d08 Mon Sep 17 00:00:00 2001 From: Rachel Date: Sun, 21 Jan 2024 13:35:18 -0800 Subject: [PATCH] tidying up last years worksheets --- .../worksheet_group_both_1.tex | 28 --- .../Worksheet_3_Lab2/Worksheet_lab2.tex | 41 ---- .../Worksheet_3_Lab2/worksheet_group_3.pdf | Bin 76492 -> 0 bytes .../Worksheet_3_Lab2/worksheet_group_3_1.jpg | Bin 466940 -> 0 bytes .../Worksheet_3_Lab2/worksheet_group_3_2.jpg | Bin 397403 -> 0 bytes .../Worksheet_4_Lab3/Worksheet_wk4.ipynb | 199 ------------------ worksheets/Worksheet_5_Lab4/Fig1.png | Bin 25029 -> 0 bytes worksheets/Worksheet_5_Lab4/Fig2.png | Bin 38568 -> 0 bytes worksheets/Worksheet_5_Lab4/Fig3.png | Bin 53468 -> 0 bytes worksheets/Worksheet_5_Lab4/Fig4.png | Bin 50870 -> 0 bytes worksheets/Worksheet_5_Lab4/Fig5.png | Bin 50690 -> 0 bytes .../Worksheet_5_Lab4/Worksheet_lab4.tex | 84 -------- .../Worksheet_5_Lab4/worksheet_group_5.pdf | Bin 281538 -> 0 bytes .../Worksheet_5_Lab4/worksheet_lab4_group.pdf | Bin 282176 -> 0 bytes .../worksheet_lab4_group_page1.jpg | Bin 321486 -> 0 bytes .../worksheet_lab4_group_page2.jpg | Bin 340289 -> 0 bytes .../worksheet_lab4_individual.pdf | Bin 282238 -> 0 bytes 17 files changed, 352 deletions(-) delete mode 100644 worksheets/Worksheet_1_intro/worksheet_group_both_1.tex delete mode 100644 worksheets/Worksheet_3_Lab2/Worksheet_lab2.tex delete mode 100644 worksheets/Worksheet_3_Lab2/worksheet_group_3.pdf delete mode 100644 worksheets/Worksheet_3_Lab2/worksheet_group_3_1.jpg delete mode 100644 worksheets/Worksheet_3_Lab2/worksheet_group_3_2.jpg delete mode 100644 worksheets/Worksheet_4_Lab3/Worksheet_wk4.ipynb delete mode 100644 worksheets/Worksheet_5_Lab4/Fig1.png delete mode 100644 worksheets/Worksheet_5_Lab4/Fig2.png delete mode 100644 worksheets/Worksheet_5_Lab4/Fig3.png delete mode 100644 worksheets/Worksheet_5_Lab4/Fig4.png delete mode 100644 worksheets/Worksheet_5_Lab4/Fig5.png delete mode 100644 worksheets/Worksheet_5_Lab4/Worksheet_lab4.tex delete mode 100644 worksheets/Worksheet_5_Lab4/worksheet_group_5.pdf delete mode 100644 worksheets/Worksheet_5_Lab4/worksheet_lab4_group.pdf delete mode 100644 worksheets/Worksheet_5_Lab4/worksheet_lab4_group_page1.jpg delete mode 100644 worksheets/Worksheet_5_Lab4/worksheet_lab4_group_page2.jpg delete mode 100644 worksheets/Worksheet_5_Lab4/worksheet_lab4_individual.pdf diff --git a/worksheets/Worksheet_1_intro/worksheet_group_both_1.tex b/worksheets/Worksheet_1_intro/worksheet_group_both_1.tex deleted file mode 100644 index c6b5fe7..0000000 --- a/worksheets/Worksheet_1_intro/worksheet_group_both_1.tex +++ /dev/null @@ -1,28 +0,0 @@ -\documentclass[12pt]{article} - -\include{latex_env} - -\rhead{Worksheet One} - -\begin{document} - -Before you begin you should have a live version of the Lab 1 jupyter notebook and have read/worked through to just above ``Example Two'' - -\begin{enumerate} -\item In your group, take the time to introduce yourselves to each other. Names of those in group: - -\vspace{2in} - -\item When I returned to my townhouse after Yule with my family, I discovered that I had not left on the heat and it was 5$^o$. I turned on the heaters, heading for a temperature of 20$^o$. I observed that after 12 hours, it had finally reached 18$^o$. What is the effective conductivity of my home? - -\vspace{0.5in} - -\item What are the units of effective conductivity? - -\vspace{0.5in} - -\item Can you change to more ``human'' units? - -\end{enumerate} - -\end{document} diff --git a/worksheets/Worksheet_3_Lab2/Worksheet_lab2.tex b/worksheets/Worksheet_3_Lab2/Worksheet_lab2.tex deleted file mode 100644 index 83d5509..0000000 --- a/worksheets/Worksheet_3_Lab2/Worksheet_lab2.tex +++ /dev/null @@ -1,41 +0,0 @@ -\documentclass[12pt]{article} - -\include{latex_env} - -\rhead{Worksheet Three} - -\begin{document} - -{\bf Names} (First only, no student numbers):\\ - - -Before you begin you should have read and worked through Lab 2. - -\noindent{\bf All questions should be done by hand (not by computer) - and show your steps.} - -\begin{enumerate} -\item Error terms in the backwards Euler -\begin{enumerate} -\item Derive the error term for the backward difference formula using Taylor series, and hence show that it is first order. -\vspace{3in} - -\item How does the constant in front of the leading order error term differ from that for the forward difference formula? Relate this back to the results plotted in the Lab (Figure error), where these two formulae were used to derive difference schemes for the heat conduction problem. (i.e., explain why backward euler is an overestimate and forward euler is an underestimate of the exact solution) -\vspace{3in} -\end{enumerate} -\item For the equation $y = sin(\lambda t)$ derive the following: -\begin{enumerate} -\item $dy/dt$ (= $y'(t)$) -\vspace{1in} -\item Write down an implicit scheme approximation for $y'(t_i)$ -\vspace{1.5in} -\item Using the approximation $sin(\alpha - \beta) \approx sin(\alpha) - \beta cos(\alpha)$ (true when $\alpha$ and/or $\beta$ follow a particular condition) show that your implicit scheme is consistent with the analytical solution. -\vspace{2in} -\item What are the conditions under which the approximation $sin(\alpha - \beta) \approx sin(\alpha) - \beta cos(\alpha)$ holds? (do an internet search if none of your group knows offhand). What do these conditions mean (qualitatively) for the accuracy of the implicit scheme from section 2b? -\end{enumerate} - -\vspace{2in} - -\end{enumerate} - -\end{document} \ No newline at end of file diff --git a/worksheets/Worksheet_3_Lab2/worksheet_group_3.pdf b/worksheets/Worksheet_3_Lab2/worksheet_group_3.pdf deleted file mode 100644 index 030d29c2131cd08cbddc37267f0edbd501c11959..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 76492 zcmdqIW0WV|lP+3zS9RI0>N0+1+qS!G+eVjdtIM`++qP}rdjB(X&YUxI?>e9EUF+tT zTstyy=Z@GBv7X3$l2lGega$y%3`5%Wl=le(U?!j^u+cY%;o>5olQOe5(z7>nH!>su ze2)lNS(w-v25G6NTBLX@#1ta5cGmNZF98C$BzgH?^X6a~T|9!U9b2Jh% zGO#iH*7~=zoSwav1HnH|5VWy$va)s{U?QNCvo|s{GjO!ACjc;fTSh>q`t1q8x4D3S z+#qgkXyp2jfSG{#Uw#p{Hnt%EFn+H?fq+iI#>SBV!1`|k#c!Vyu(1AXM(2Ndiuu2I zhfZ9GK$FXWiJ6U^nU#gXm`#tF9l*xIYQSvFz+lY6Vx-4t0HEjLVr5`v(PuDVW@7~a z7!8e$*yxRz=ot)I^#R|idMpM!zyH|;2SdpOO&3_I>?79`$cZvijzVj#mF8FBs@q82@iF zLxzCqy9|h!**iFX=Q`kj39AY<3&pizqz`YO0Z+JwAkn+5l2r-RL%aANG1M_Z6DmAV z#C#2n2g~*XmsMRwqH#1Y;47AX1#b8E8JBZ&=HePj^d~8^QtrQy96^v_K%qam6+smJ zC`KZL6afaL&}%{fqm+d-iZM%iI15h@@u~Kn)oxF*6qy|4@CIE0wt;#>0ho1E7C@R_ ziyW{^U!Wh6m7Pm7=dTP~DbRSvV^AeAoB(4)dg~lIpvG9KUl7G8@ho5viIll++wwmL z6%LTc;FL(0`(62b8IY?RK)w0ufgzwQW4o!BLnBjyB=%6x`xLgD>QTa}mB1;!?#`+r z@N2rN+1Fiqp2f9mry_J1KDTyDb*pqlL*wwwEMOjC;%Gy+6`!5a#r4Qxm5L zcyTi6y%V`(OEm;NqSJYK0c0rwGW6I2j=hWSvQ)E)hWAKdXdYG~k1`^hP8p+IQfc@=heX)A+iUTID zJk~+QA7ZaJmP(WOq?A!rtGsKwwG)w2Dzt7C?Il@5&M{1v{&4YWzj{)&qkZR2v6|1?wEUG9D97EXc+_ z$Da+hY{W}oyKW8La`ruS^*n3LVbo|s&75kjIHB(13K^KiAdJgmO$Tukz6S5PxjdiS zIT@e}HZidYvb>|~$NC!l#Q5^&{HT@wLYf#kczBp$pVo5hv4j%YQ|(^PR1>PjjZljm zsD!ne?hq>fvx{{9axyV=Ch6PxKIg*s_JEvF?)xhhH|M~4dW10tc>!4rca0A}8~69R zXIQ%nUwD6c+iJzFjKG>+a7D4xa-;_5T0H-S?Zef_R#bkO@a&%sLY`h2(-!2qpKJVY z8#x6_++2RiDPQ`NEm@+OtN4n2d-?7hqx)axpa{zusSdkM#Qppt8^? zdU$N6+%VJ;8Z-pB)e6?lEG!@G!L8nwvw~%>&-CLd`VmRO;2!i?qtwG57U%0F z)KDy7iV4Hq#9i;S;a7XamHA3k@6T^L@>!5ogKli9y`q9M@Ppqm7J1glJOk>6aXgNCo$dJ8_nYaLz%KKF7!5=dW6`9#?<}7DZRC zGLH;n{Z;r&!o2qcdG@WH3`l^!TEt#F)f;`*8KqosZy6?dhU6NAK8< ztT&qbX2X|0*Y5O$c(&lh0gt&x|Gb5v?AzSQ7@kRRITWLkt>IjRLr!;ncPpyMZgE23 z8+~AE|G!V<0&}A8x6V7q(2bLkT zsZHUa-V9}5AXd8Q+C8zoO}SkwmwLgSdZEYN*eviIH&JHUA^qwM?#otgeFUfA#4JQ8 zmMEnx*rLmdsd>B+XqV**73vi?^{hOUz115`OXj?vnv-u-dFY~<)8k>o;N^41$4t{n zS~-qR@lAS=D{I_kZD4k-XL6beAD_@Mj+k!%xX!6Fid13E(HJ!?3$)yBHIN#gAAsgP zc)AiA%!u{)KUuJ(DPycRBIt1kRTXDt2|2A1Dpa}~ z4nY=2#!_o{H~zkZ&%91@v90CUJh>C}?vH+f_UV(|DSLVc?b=R$5A)eyYB+9DjUB7X2AV&Ut$?z9cLAFbazKt6_QWYK0{i>BJ8V;=56p)`fN2Kqq z=BO&Y!bnV6&cE6p>s&XGXm~Y`?#!TjbC2#!qI+8wVb!@@kW&OO2wD!;dl*m{lwc``$#%CM~ z*XF-M#qYl0f8vh+7IrHVFn#0Ue+TC*|7slmCuY^v)iu!F7B|o})*XJC>Yf4u*JVK# zOYjr+_lrFU=tcQC;tOOcH{KmH)IHR#+oj-N@;rv+1PTFUJq|8f#FH z`LtOyB#bO=ye;%uKX?uF5QR6hcGp%c3kB;v+$ReExZVk@^H?$y#4D@uky#}A9Kjbo=rXR2 z#1S{H@6$F1rF)q&C6Ev|(y$~Xul1pemXQ3~RaciiH|iDkJRJnzsvmufEL!6jQGZ8( znRTGCXe|>ZqJ?(R-4jK!F>k0XTEyp>_mJJk^rIIH7dF#2CS7wkxq97{^l6%v%EX$m z=z83j&KJphoa))zM$2O_HS_k8>syggAl411=i?QzC1i`!>K{GzZQ;T`dS|{EQ?iH3 z)#7|75AfT1_kHy4z8*hvR%TKqA>wXA*GvX~LD6GmUI zOjadXSHK`k3s=41JJZX2BzZr$mZ>n^YnZuPokvC_@+ke0vG~M!nT#bB7ew3p(RrrZy$Bl7NXEQ6R_xbjRDZRL02y%oYQ(r7lS2r zIVM^I@e}R}+bhsFmUOFWhm?=A((zq>Aq;N?yyPtlPzZ!`js}4B1Dm^))+pZuo(x>c zmvt))4TR&hjtK@fO)3(US*XY@nt;=2BX&{Z`FEyK>mEXhqp#D%ZI%|x9sf%1c1@I| zW8x$75ubIc3FRH>%sMtUM>PFgO&LzA6MF!D2aftT@ z>{e@?RFN7CUKc=Y|9dc5XH|~xZ+l<=SJQJ~(G1?~hSewg;W(uPO?1oTk?{wx1fbXJtClLx zxX$`eU%5fp;<;XsPQeNsSep*IZq7#sEtQ?;f~SJp-9

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+0,0 @@ -\documentclass[12pt]{article} - \usepackage{caption} -\usepackage{subcaption} -\include{latex_env} - -\rhead{Worksheet Four} - -\begin{document} - -{\bf GROUP WORKSHEET - TO BE HANDED IN} - -%{\bf INDIVIDUAL WORKSHEETS - not for handing in} -{\bf Names} (First only, no student numbers):\\ -\vspace{0.5in} - -Before you begin you should have read and worked through Lab 4. - -\noindent{\bf All questions should be done by hand (not by computer) - and show your steps.} - -\begin{enumerate} -\item Local and Global Errors -\begin{enumerate} -\item The figure below solves the system $\frac{dy}{dt} = -y + t + 1$ with the initial condition $y(0) = 1$; this has an exact solution $y(t) = t + e^{-t}$. For scheme 1, label the global and local errors at $t = 1.0s$. -\begin{center} -\includegraphics[width=10cm,height=8cm,trim={0cm 0cm 0cm 0},clip]{Lab4_WS_fig1.png} -\end{center} -\vspace{0.25in} -\item For scheme 1, label the global error and your best estimate of the local error at $t = 2.0s$ on the figure . -\vspace{0.25in} - -\item Which scheme do you think is most likely to be the highest order. Give your reasoning below, including how certain you are. What extra information would help you know for sure (beyond knowing what the schemes are!)? -\vspace{2in} -\end{enumerate} -\item Errors and scheme order -\begin{enumerate} -\begin{center} -\includegraphics[height=5.5cm,width=5.5cm,trim={20cm 0cm 0cm 0},clip]{Lab4_WS_fig2.png} -\end{center} -\item For the figure above, what is the global error for $dt = 0.1$ and $dt = 0.2$ at $t=2.0$ ? -\vspace{0.4in} -\item What is the order of the global error? What is the order of the scheme? -\vspace{0.4in} -\end{enumerate} - -\item Comparing schemes -\begin{enumerate} -\item From the 3 figures below (which have the y axis values removed deliberately), rank the schemes by their order, O$(\Delta t^?$), from highest to lowest. -\vspace{0.25in} - -\begin{figure}[h!!] - \centering - \begin{subfigure}[b]{0.32\textwidth} - \centering - \includegraphics[height=5cm,width=\textwidth]{Lab4_WS_fig3.png} - \caption{scheme A} - \label{fig:y equals x} - \end{subfigure} - \hfill - \begin{subfigure}[b]{0.32\textwidth} - \centering - \includegraphics[height=5cm,width=\textwidth]{Lab4_WS_fig4.png} - \caption{scheme B} - \label{fig:three sin x} - \end{subfigure} - \hfill - \begin{subfigure}[b]{0.32\textwidth} - \centering - \includegraphics[height=5cm,width=\textwidth]{Lab4_WS_fig5.png} - \caption{scheme C} - \label{fig:five over x} - \end{subfigure} - \caption{Absolute error $|numerical - analytic|$ for three different numerical schemes. Black horizontal line is the $y=0$ axis.} - \label{fig:three graphs} -\end{figure} -\item By looking at how the global error scales with dt, estimate the order of each scheme. - -\vspace{0.3in} -\end{enumerate} -\item Optional extra question if time: repeat the analysis for Q3b with the local error. - -\end{enumerate} - -\end{document} \ No newline at end of file diff --git a/worksheets/Worksheet_5_Lab4/worksheet_group_5.pdf b/worksheets/Worksheet_5_Lab4/worksheet_group_5.pdf deleted file mode 100644 index 4519da574fa561a7fa7cb7b99b79d77dc7c8b664..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 281538 zcmeFYWmHyc)Hb?BknZjfkdSUk>267B9=fC@rAtyt=?>|V7U}L5q`MnL_-@p_-TVE% zbAFw1&Y$xPhm0rITKAgwjB8%kTvUpp;tVW|90*h`7n!#RESzM_WVVJD2z-2GOtR)S z5CeO2H;6GA3wTGy%FV*T#!bc~Nv2K4#?8h?#=^x;rbEW0K*kEb7bD~0;o)E>W0EIh zC1X;(|MmU%0s;sS8{_*^lKsETmOdZY0SeU^|#m%i8 zA@<;}m4PEf6k=p+41V_OucCpywFB9`6+~>UoUCme$T-ND6zw6#=0=XT_GB!q;Ks<9 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