1+1

(Sqrt[5])

(Sqrt[4])

(Sqrt[5.])

N[(Sqrt[5])]

N[(Sqrt[5]),25]

N[2,2]

(5^2)

LaplaceTransform
function=25

function*2

Solve[(x^2)+2*x+5*t==1,x]

t=5

list={1,5,{3,2},4,6}

list[[3,2]]

FullForm[list]

N[Sin[Cos[(E^Pi)]]]

t

t=25

ClearAll[t]

mySolve=Solve[(x^2)+2*x+5*t==1,x]

mySolve[[1]]

Plot[(E^x)*(E^(Sin[(x^2)])),{x,0,6Pi}]

mySolve=Solve[(x^2)+2*x+5*t==1,x]

x=x/.mySolve[[1]]

Plot[-1-(Sqrt[2-5 t]),{t,-5,5}]

ClearAll[x]
myRules={x->10,x->2,x->3}

x/.myRules

myRules2={x->1,y->2,z->3}

{x+y,y,y+a}/.myRules2

mySolve=Solve[5*x==1,x]

Plot[x/.mySolve,{x,1,5}]

myList={1,5,4,6,8,9}

myList[[-1]]

Length[myList]

Sort[myList]

N[(Sqrt[5])]

(Sqrt[5])//N

N@(Sqrt[5])

(*Second lecture*)

sol={x,y}/.Solve[{x+y-t==2,x+t-y==5},{x,y}][[1]]

t=2;
Plot[sol,{t,2,5},PlotLabel->"My Plot",AxesLabel->{"t","f1(t),f2(t)"},PlotStyle->{{RGBColor[0,0,1], Thick,Dashing[0.02]},{Thickness[0.01],Red}}]

??Plot

pl1=Plot[{Sin[(E^x)]*(E^x),Cos[(E^x)]*E},{x,1,10},PlotStyle->{{Blue,Thick,Dashed},{Red,Thickness[0.001]}},AxesLabel->{"x","sin[(E^x)]*(E^x),cos[(E^x)]*E"}]

SetDirectory[NotebookDirectory[]]

Export["graph.jpg",pl1,ImageResolution->400];

ClearAll[t]
Manipulate[Plot[Sin[k*t],{t,0,2*Pi},PlotStyle->Thick,PlotRange->{Automatic,{-2,2}}],{k,1,50}];

Print["It is OK!"];

sol=Solve[(x^2)+a*x+5==0,x];
x1=x/.sol[[1]];
x2=x/.sol[[2]];
Print["x1 = ",x1," x2 = ",x2 ];

DSolve

Series[Sin[x],{x,0,15}]

n=5;
(∑_(i=0)^n)(Subscript[a, i])*(x^i)==0
Solve[%,x]

DSolve

DSolve[y'[x]+(x^2)*((y[x])^2)==x Sin[x],y[x],x]

dsol=y[x]/.NDSolve[{y'[x]==y[x]*Cos[x+y[x]],y[-5]==1},y[x],{x,-5,30}][[1]]

Plot[dsol,{x,-5,30},PlotRange->All]

??NDSolve