1+1

Sin[25.]

{1,6,5}

(5-(3+Sin[x]))

myvar=5

N[Gamma[3.3],50]

(Sqrt[2])

(Sqrt[4])

(Sqrt[2.])

N[(Sqrt[2]),100];

var=5;

var =5

(*vari=5*)

vari
var

(Sqrt[6])(*ctrl+2*);
(5^6) (*ctrl+6*);
(7/6)(*ctrl+/*);

∫(t^7)*(E^t)\[DifferentialD]t

DSolve[y''[t]+3*y'[t]+6*y[t]==Sin[t],y[t],t]

vari=5
Solve[vari==5]

Solve[varib+3==5]

vari=6
vari==5

DSolve[y'[t]==6,y[t],t]

Solve[5+y==3,y]

Solve[{x+y==3,x-y==5},{x,y}]

1 2

∫Sin[x]*Cos[x]\[DifferentialD]x

myLap=LaplaceTransform[(((Sin[t]))^4),t,s]

myInvLap=InverseLaplaceTransform[myLap,s,t]

t=5;
Plot[Sin[x],{x,0,6Pi},AxesLabel->{"t [s]","sin(t) "},PlotLabel->"Current",PlotStyle->{Thick,Dashed,Red}]

DSolve[{y'[t]+5*y[t]==Sin[t],y[0]==3},y[t],t]
ClearAll[t]
sol=y[t]/.DSolve[{y'[t]+5*y[t]==Sin[t],y[0]==3},y[t],t][[1]]

a/.a->3

b/.{a->3,b->2}

Plot[sol,{t,0,6Pi},AxesLabel->{"t [s]","sin(t) "},PlotLabel->"Current",PlotStyle->{Thick,Dashed,Red}]

TreeForm[{1,2,5,{3,1},6}]

{1,2,5,{3,1},6}[[4,3]]

(*second lecture*)

myVar=DSolve[{y''''[t]+10*y''[t]+9*y[t]==Sin[t],y[0]==1,y'[0]==-1,y''[0]==2,y'''[0]==-2},y[t],t]

someN={1,4{1,3},{2,3,1},1}

TreeForm[someN]

someN[[2,3]]

PlotRes=y[t]/.myVar[[1]]

x=5.

Manipulate[Plot[{PlotRes,1.5Sin[t]},{t,0,6Pi},AxesLabel->{"x","Sin[s]"},PlotLabel->"My plot",PlotStyle->{{Hue[b], Thickness[0.01], Dashed},{RGBColor[0.5,0.2,0.2],Thick}}],{b,0,1}]

myVar[[1,1]]

{{5,3}}//TreeForm

data=Table[{i,(i^2)},{i,2,10,0.1}];

ListPlot[data,PlotStyle->{PointSize[0.01],Orange},Joined->True,PlotLegends->"some"]

Plot[Sin[x],{x,0,10},PlotRange->{{0,50},{0,1}},Grid]

ListPlot[Table[{(E^x),(Sqrt[x])},{x,1,10,0.1}],AxesLabel->{"Axis x","Axis y"},PlotLabel->"My plot",PlotStyle->{Green, PointSize[0.01]},PlotLegends->"Line"]