1+1

(Sqrt[5])

(25^(1/4))

N[(Sqrt[5])]

N[(Sqrt[5]),100]

(Sqrt[5.])

N[(Sqrt[5])]
(Sqrt[5])//N
N@(Sqrt[5])
N[(Sqrt[5]),10]
(Sqrt[5])//N[#,10]&
N[#,10]&@(Sqrt[5])

InverseLaplaceTransform

2 3

2 6

1 kyncl
1.kyncl

petr42Skupina8={1,2,6};

x=5;
ClearAll[x]
D[f[x],x]
Solve[(x^3)==1,x]

kyncl=0;

?@

Not[c]&&b||c&&b//Simplify

rce=(x^5)+x-17.==0;
Solve[rce,x]

?===

?=

?:=

ClearAll[f];
f[x_]=Integrate[(x^3)*Sin[(1/x)],x]
f[1.]

ClearAll[f];
f[x_]:=Integrate[(x^3)*Sin[(1/x)],x]
f[1.]

difrce=y''[x]+b*y'[x]+y[x]==0;
DSolve[difrce,y[x],x]

??Plot

Plot[{Sin[(x^2)],Cos[(x^2)]},{x,0,2(Sqrt[Pi])},PlotStyle->{{Red,Thick},{Blue,Thick}},AxesLabel->{"x","f1,f2"}]

(*******zde zacina druhe cviceni********)

List[a,b,c]

{a,c,b}

listik={5,4,{alfa,romeo},{{2},1}};

listik[[-1]][[1]]
listik[[-1,1]]

Length[listik]

TreeForm[listik]

Range[10]

Table[mesicek,{12}]

Table[(x^i),{i,10}]

Table[(x^i),{i,0,10}]

Table[(x^i),{i,8,10.4,(1/2)}]

mocniny=Table[(x^i),{i,1,7,0.1}];
Plot[mocniny,{x,0,1}];

Table[i+(E^j),{i,4},{j,4}]
%//MatrixForm

Table[i+(E^j),{i,4},{j,4-i}]
%//MatrixForm

{a,b,c}.{1,2,3}

{a,b,c}*{1,2,3}

(x^2)/.x->2

(x^2)+y/.{x->2,y->x}

(x^2)/.{x->2,x->1}

Range[10]+5
%/.{9->Pi}
%/._?EvenQ->E

res=Solve[(x^2)-5x+4==0]
(x^2)/.res

(x^2)/.{{x->1},{x->4}}

(x^2)/.{x->1,x->4}

tiskni[[2]]

rovnice=(x^2)-((t^2)-1)*x-t==0;
dos=Solve[rovnice,x];
tiskni=Re[x]/.dos;
Plot[tiskni,{t,-1,1},AxesLabel->{"t","Re[x1],Re[x2]"},PlotStyle->Thick]
Plot[tiskni[[1]]-tiskni[[2]],{t,-1,1},AxesLabel->{"t","Re[x1]-Re[x2]"},PlotStyle->Thick]

?f1

ClearAll[f1,f2,x];
f1[x_]:=Integrate[(x^2)*Sin[x],x]
f2[x_]=Integrate[(x^2)*Sin[x],x]

f2[Pi]

Fibonacci[8]

?a

ClearAll[a];
a[0]=0;
a[1]=1;
a[n_]:=a[n-1]+a[n-2];
Timing[Table[a[i],{i,25}]][[1]]

ClearAll[a];
a[0]=0;
a[1]=1;
a[n_]:=a[n]=a[n-1]+a[n-2];
Timing[Table[a[i],{i,25}]][[1]]

Trace[a[26]]

(**********treti cviceni********)

ClearAll[f];
f[x_]:=0/;x≤0;
f[x_]:=x/;0<x≤1;
f[x_]:=2-(x^2)/;1<x≤(Sqrt[2]);
f[x_]:=0/;x>(Sqrt[2]);
Plot[f[x],{x,-1,2},PlotStyle->Thick]

ClearAll[f];
f[x_]:=1-(x^2)/;-1<x≤1;
f[x_]:=f[x+2]/;x≤-1;
f[x_]:=f[x-2]/;x>1;
Plot[f[x],{x,-4,4},PlotStyle->Thick]

Trace[f[5.5]];

Sin[{ja,ty,on}]
Map[Sin,{ja,ty,on}]

ClearAll[f];
Map[f,{ja,ty,on}]
f/@{ja,ty,on}

ClearAll[f];
Apply[f,{ja,ty,on}]
f@@{ja,ty,on}

Range[100]

Plus[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100]

Plus@@Range[100]
Apply[Plus,Range[100]]

?&

test[x_]:=x>10;
cisla=Range[20]
Select[cisla,test]
Select[cisla,#>10&]

((#)^2)&[5]
((#)^2)&/@Range[10]

?NDSolve

s=NDSolve[{y''[x]+y'[x]+Sin[y[x]]==0,y[0]==0,y'[0]==1},y,{x,0,30}];
Plot[Evaluate[y[x]/.s],{x,0,30},PlotRange->All]

s=NDSolve[{y''[x]+y'[x]+Sin[y[x]]==0,y[0]==0,y'[0]==1},y,{x,0,30}];
Plot[Evaluate[y[x]/.s],{x,0,30},PlotRange->All]

s

x/.Solve[x==5][[1]]

x0=0.;
y0=1;
xmax=5;
n=300;
Δx=(1/n)*(xmax-x0);
derivace[x_,y_]:=-.3(1/(x+1))-y;
EuleruvKrok[{x_,y_}]:={x+Δx,y+Δx*derivace[x,y]};
reseni=NestList[EuleruvKrok,{x0,y0},n];
pl1=ListPlot[reseni,PlotRange->All];
proDSolve={y'[x]==derivace[x,y[x]],y[x0]==y0};
tiskDSolve=y[x]/.DSolve[proDSolve,y[x],x][[1]];
pl2=Plot[tiskDSolve,{x,0,xmax},PlotStyle->{Thick,Red},PlotRange->All];
Show[pl1,pl2]

ClearAll[fi]

Manipulate[R=100;
L=0.1;
u=230*(Sqrt[2])*Sin[314t+fi];
rce={R*i[t]+L*i'[t]==u,i[0]==0};
tmax=0.08;
res=NDSolve[rce,i[t],{t,0,tmax}][[1]];
Plot[i[t]/.res,{t,0,tmax},AxesLabel->{"t[s]","i[A]"},PlotStyle->Thick],{fi,-Pi,Pi}]