1+1
1+2

%

a=4

2%

a=3

a=5

a

(*Math. is case sensitive*)
Sin[Pi]
sin[Pi]

b=1

ClearAll[b]

?b

Sin[5]

Sin[5.]

(1/7)+(2/13)

(1./7)+(2./13)

(*enumerates result*)
N[Pi]

N[Pi,100]

(*names of vars cannot start with numbers*)
kyncl123
123

(*space means multiplication*)
i am an idiot

a=23*7+p;

expr=(x^2)+2*Sin[α*t+(ϕ/6)];
FullForm[expr];
TreeForm[expr];

b*c=2

FullForm[b*c]

Plot[x*Sin[(1/(1+x))],{x,1,20},PlotRange->All];

x=1

ClearAll[x,y]

Solve[x+25y==1&&x-y==5,{x,y}]

Solve[{x+25y==1,x-y==5},{x,y}]

DSolve[D[y[x],x]+Sin[y[x]]==0,y[x],x]

(*Solve fcn does not solve nonlinear equations without exact solutions*)

Solve[Cos[x]==x,x]

(*FindRoot does it numerically!*)

FindRoot[Cos[x]==x,{x,0}]

list={1,2,4}

FullForm[list]
TreeForm[list]

ClearAll[a]

vec={1,3,4}

vec2={a,b,c}

vec.vec2
vec*vec2

mat=(({{1, 2, 5}, {3, 4, 6}, {3, 4, 7}}))

mat.vec2

Det[mat]

alist={1,2,5,35,7,4}

alist[[3]]

Part[alist,3]

listoflist={1,2,4,{2,5,{34,1}}}

TreeForm[listoflist]

listoflist[[4,2]]

Last[listoflist]

First[listoflist]

listoflist

listoflist[[-2]]

Length[listoflist]

Table[dalmatin,{i,1,101}];
Table[x^i,{i,10}]
Table[x^i,{i,1,10,1.7}]
Table[x^i,{i,{1,5,7,8}}]

listofOddPowers=Table[x^i,{i,1,15,2}]

Options[Plot];

Plot[listofOddPowers,{x,-1,1},PlotRange->Full]

Plot[listofOddPowers,{x,-1,1},PlotRange->{{0,1},All}]

Plot[listofOddPowers,{x,-1,1},PlotRange->Full,AxesLabel->{"x","y"}]

Plot[{Sin[x],Cos[x]},{x,-Pi,Pi},AxesLabel->{"x","Cos Sin"},PlotStyle->{{Blue,Dashed},{Red,Thickness[0.02]}},GridLines->{{Pi,2Pi},{-0.1,-.5,.5,0.1}},PlotLegends->"Expressions"]

Manipulate[
Plot[{Sin[x],Cos[n*x]},{x,-Pi,Pi},AxesLabel->{"x","Cos Sin"},PlotStyle->{{Blue,Dashed},{Red,Thickness[0.02]}},GridLines->Full,PlotLegends->{"Sin[x]","Cos[n*x]"}],
{{n,2},1,3}]

Manipulate[
ParametricPlot[{t+rc*Cos[t],rs*Sin[t]},{t,0,4Pi},PlotRange->Full,AxesLabel->{"x","y"},PlotStyle->Blue],
{rc,1,6},{rs,1,6}]

plts=Table[Plot[listofOddPowers[[i]],{x,-1,1}],{i,Length[listofOddPowers]}];

Show[plts]