MathematicaBasic.txt

(* THE VERY BASIC (1) *)

5/6
3+4
9^2
E^(I Pi)
Pi
N[Pi]

(* THE VERY BASIC (2) *)

3 + 4
%/2
N[%]
10*10 == 100
10 < Exp[10]
10 < Log[10]

(* THE VERY BASIC (3) *)

(x - 1) (x + 1)
Simplify[%] 

(x + 1) (x + 2) (x + 3)
Expand[%]

x^10 - 1
Factor[%]

=============================================================================

(* DEFINITION *)

a = 1
b = 2
a + b
a*b
y = Sin[x]
Plot[y, {x, -Pi, Pi}]

(* The last command (Plot[y,{x,-Pi,Pi}]) is not recommended. Instead, you should define a function. *)

f[x_] := Cos[x]
f[Pi]
f[Pi/2]
Plot[f[x], {x, -Pi, Pi}]

=============================================================================

(* Substitution (VERY IMPORTANT!) *)

y = Sin[x] + Cos[x]
y /. {x -> 4}
y /. Sin -> Tan
y /. {Sin -> Exp, x -> 4}
ReplaceAll[y, x -> 4]

(* /. is a syntax suger of ReplaceAll. *)

(* REPEATED substitution *)

energy = m*gamma
ReplaceAll[energy, {gamma -> 1/Sqrt[1 - beta^2], beta -> v/c}]

ReplaceRepeated[energy, {gamma -> 1/Sqrt[1 - beta^2], beta -> v/c}]

(* ReplaceRepeated has a syntax sugar //. *)
energy //. {gamma -> 1/Sqrt[1 - beta^2], beta -> v/c}

=============================================================================

(* EMERGENCY EXIT *)

(* ALT (or command)+period if you want to stop evaluation. *)
(* You can stop evaluation from the menu: Evaluation>Abort Evaluation. *)

Integrate[(Sin[x] + Tan[x])^100, x]

(* This is important when you induce an infinite-evaluation. *)

Sin[x] /. x -> Sin[x]
Sin[x] //. x -> Sin[x]

=============================================================================

(* THAT'S MATHEMATICA BASIC. *)
(* Now Let's forget all == ABORT THE KERNEL. *)

energy

Exit[]
(* Now the kernel has been initialized. Everything is now cleared. *)

energy
(* is now undefined. *)

(* Note that you can clear a variable with Clear *)
abc = a + b + c
{a, b, c} = {1, 2, 3}
abc

Clear[a]
abc

Clear[b,c]
abc