1+1

(Sqrt[5])

(25^(1/4))

N[π]

N[π,40]

N[Pi]
Pi//N
N@Pi
Pi//N[#,30]&
N[#,30]&@Pi

?Inverse*;

1kyncl

(x^3)
(2/4)
(Sqrt[5])

αβ

?Solve

Solve[(x^5)+x-17==0]//N

x*4
x 4
4x

DSolve[(1+(x^2))y''[x]+x*y'[x]+(4-(x^2))*y[x]==0,y[x],x]

Simplify[(Sqrt[x])*((Sqrt[y])/(Sqrt[u])),{x>0,y>0,u>0}]

1.*60!

Solve[(x^2)+3x+8==0.]

Plot

Plot[Tanh[100Sin[x]],{x,-15,15}]

Plot[Tanh[(10^(-4))Sin[x]],{x,-10,10}]

Plot[Tanh[(10^(-4))Sin[x]],{x,-10,10},PlotRange->{{0,16},Automatic},PlotPoints->300]

Plot3D[Arg[x+I*y],{x,-10,10},{y,-10,10},PerformanceGoal->"Quality"]

Plot[Erfc[x],{x,0,5},PlotRange->All,PlotStyle->{Thick,Pink},AxesLabel->{"x","erfc[x]"}]

Plot[{Erfc[x],Erf[x]},{x,0,5},PlotRange->All,PlotStyle->{{Thick,Red},{Thick,Blue}},AxesLabel->{"x","erfc[x],erf[x]"}]

(x^5)+Exp[-x]+Sin[a+b]//SpokenString

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

listik={1,maso,{alfa,romeo},{1,{{-2}}}};
listik[[3]][[1]]
listik[[3,1]]

listik={1,maso,{alfa,romeo},{1,{{-2}}}};
listik[[-1,-1,1,-1]]

listik//TreeForm

(x^2)/.x->2

?/.

Range[10]
%/._:>Pi
%%/._?EvenQ:>Pi

{x,y,Muller,Kyncl}/.Muller->Kyncl

{x,y,Muller,Kyncl}/.{Muller->Kyncl,Kyncl->x}

{x,y,Muller,Kyncl}/.{Muller->Kyncl,x->Kyncl}

x/.{x->1,x->2}

x/.{{x->1},{x->2}}

dosad={podstava->10(cm^2),vyska->10cm,cm->0.01,objem->podstava*vyska};

(5*objem/.dosad)
%/.dosad
%/.dosad

5objem//.dosad

x+2y//.{x->y,y->x}

Range[1]

rce=(x^2)+3x+5==0;
vyraz=(x^2)-3x+5

dosadzaiksy=Solve[rce,x]

vyraz/.dosadzaiksy//N
vyraz/.dosadzaiksy[[1]]//N
vyraz/.dosadzaiksy[[2]]//N

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

rce=3(x^2)+t*x+(1/t)==0;
res=Solve[rce,x];
koreny=(x^2)/.res;
tisknout=koreny[[2]]+koreny[[1]];
Plot[tisknout,{t,1,4},PlotStyle->{Green,Thick},AxesLabel->{"t","(x1^2)+(x2^2)"}]

Range[10]

Table[opice,{12}]

Table[(opice^i),{i,12}]

Table[(opice^i),{i,4,12}]

Table[(Pi^i)*(E^(4-i)),{i,11,12,(1/10)}]

Table[(Pi^i)+(E^j),{i,5},{j,5-i}]

%//MatrixForm

listik=Table[(Pi^i)*(E^(4-i)),{i,11,12,(1/10)}]
n=Length[listik];
(∑_(i=1)^n)listik[[i]]

listik=Table[(Pi^i)+(E^j),{i,5},{j,5-i}];
Length/@listik

?f2

x=5;
ClearAll[f1,f2,x];
f1[x_]:=(x^2)
f2[x_]=(x^2)
f1[2]
f2[2]

ClearAll[a];
a[0]=0;
a[1]=1;
a[n_Integer]:=a[n-1]+a[n-2];
Table[a[i],{i,1,15}];
ListPlot[%];

Trace[a[5]];

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

ClearAll[f];
f[x_]:=Tanh[x]/;-3<x≤3;
f[x_]:=f[x+6]/;x≤-3;
f[x_]:=f[x-6]/;x>3;
Plot[f[x],{x,-15,15},PlotRange->All,PlotStyle->{Thick,Pink},AxesLabel->{"x","erfc[x]"}]

Map[g,{ja,ty,on}]
g/@{ja,ty,on}

Apply[g,{ja,ty,on}]
g@@{ja,ty,on}

Plus@@Range[100]

nadruhou[x_]:=(x^2);
mocniny=nadruhou/@Range[10]

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

test[x_]:=x>25;
Select[mocniny,test]
Select[mocniny,#>25&]

Manipulate[
uz=10*Sin[314t+0.8];
R1=100;
R2=100;
L=0.1;
c=100*(10^(-6));
rceUzel={iR1[t]+iL[t]==iR2[t]+ic[t]};
rceSoucastek={uz-u1[t]==iR1[t]*R1,u1[t]==iR2[t]*R2,ic[t]==c*u1'[t],uz-u1[t]==L*iL'[t]};
rcePocPodminek={u1[0]==u10,iL[0]==iL0};
tmax=0.08;
dohromady=Union[rcePocPodminek,rceSoucastek,rceUzel];
nezname=Cases[dohromady,_Symbol[t],{0,∞}]//Union;
res=NDSolve[dohromady//N,nezname,{t,0,tmax},StartingStepSize->(10^(-9))][[1]];
Plot[u1[t]/.res,{t,0,tmax},PlotRange->{Automatic,{-18,18}},PlotStyle->{Thick,Blue},AxesLabel->{"t[s]","u1[V]"}],{u10,-20,20},{iL0,-0.1,0.1}]

(*pom=Union[rceSoucastek,rceUzel];
derivace=Cases[pom,_'[t],{0,∞}];
neznBezder=derivace/.a_'[t]:>a[t];
bezder=Complement[nezname,%];
noverce=Solve[pom,derivace,bezder][[1]]/.(a_->b_):>a==b;
NDSolve[Union[noverce,rcePocPodminek],neznBezder,{t,0,tmax},StartingStepSize->(10^(-9))]
*)

ω=314;
uz=10*Sin[ω*t+0.8];
R1=100;
R2=100;
L=0.1;
c=100*(10^(-6));
rceUzel={iR1[t]+iL[t]==iR2[t]+ic[t]};
rceSoucastek={uz-u1[t]==iR1[t]*R1,u1[t]==iR2[t]*R2,ic[t]==c*u1'[t],uz-u1[t]==L*iL'[t]};
tmax=0.08;
dohromady=Union[rceSoucastek,rceUzel];

rceHUS=dohromady/.{a_'[t]:>a*I*ω,a_[t]:>a,a_*Sin[b_+c_*t]:>a*(E^(I*b))};
u1HUS=Im[(u1/.Solve[rceHUS][[1]])*Exp[I*ω*t]];

Manipulate[
uz=10*Sin[314t+0.8];
R1=100;
R2=100;
L=0.1;
c=100*(10^(-6));
rceUzel={iR1[t]+iL[t]==iR2[t]+ic[t]};
rceSoucastek={uz-u1[t]==iR1[t]*R1,u1[t]==iR2[t]*R2,ic[t]==c*u1'[t],uz-u1[t]==L*iL'[t]};
rcePocPodminek={u1[0]==u10,iL[0]==iL0};
tmax=0.08;
dohromady=Union[rcePocPodminek,rceSoucastek,rceUzel];
nezname=Cases[dohromady,_Symbol[t],{0,∞}]//Union;
res=NDSolve[dohromady//N,nezname,{t,0,tmax},StartingStepSize->(10^(-9))][[1]];
Plot[{u1[t]/.res,u1HUS},{t,0,tmax},PlotRange->{Automatic,{-18,18}},PlotStyle->{Thick},AxesLabel->{"t[s]","u1[V]"}],{u10,-20,20},{iL0,-0.1,0.1}]

Options[Plot3D];

vyr=(Sqrt[(x^2)+9(y^2)]);
Plot3D[vyr,{x,-5,5},{y,-1,1}]

RegionPlot[0.5<vyr<1,{x,-2,2},{y,-2,2}]

D[vyr,x]