1+1
2+3

a=3

a=2

a=

a

a=345;
b=0

(a^b);
(a^b);
a^b;

a=9

ClearAll["Global`*"]

Remove

kyncl je vul

1 2

a*b

Out[29]/f

%

%/.a->4

Clear[a]

vyraz=a*b;
vyraz/f
%^h

((a b)/f)

a=4

Sin[0]
Cos[Pi]
Exp[a]

0.1//Tanh

Tanh[0.1]

Sin[5]

Sin[5.]

N[Pi]

N[Pi,100]

Integrate[(E^(a*(x^2)+b*x+c)),x]

Plot[ξ*Sin[ξ*(1+ξ)],{ξ,0,12}]

Plot[ξ*Sin[ξ*(1+ξ)],{ξ,0,12},AxesLabel->{"ξ","f[ξ]"}]

ξ=hunk+knaf;
Plot[ξ*Sin[ξ*(1+ξ)],{ξ,0,12},AxesLabel->{ξ,f[ξ]}]

δΔ

Plot[ξ*Sin[ξ*(1+ξ)],{ξ,0,12},AxesLabel->{"ξ","f[ξ]"}]

Plot[ξ*Sin[ξ*(1+ξ)],{ξ,0,12},AxesLabel->{"ξ","f[ξ]"},PlotStyle->{Blue,Thick},PlotLabel->"Graf",GridLines->Automatic]

Options[Plot];

ParametricPlot[{t+Cos[t],Sin[t]},{t,0,4Pi},PlotStyle->{Red,Thickness[0.006]},AspectRatio->0.5,AxesLabel->{"x","y"},PlotLabel->"kotaalniczka"]

FindRoot[Exp[x]==2*Cos[x],{x,0}]

ClearAll[x]
rce=x==2*Cos[x]+x+0.3;
FindRoot[rce,{x,1}]

rce

(*zacate druheho cvika*)
ClearAll["Global`*"];
f[x_]:=(Sqrt[x])*Sin[(x^(3/2))+1];
Plot[f[(Sqrt[t])],{t,1,30},AxesLabel->{"t",f[(Sqrt[t])]},PlotStyle->{Red,Thick},GridLines->Automatic]

f//TreeForm

ClearAll["Global`*"];
f[x_]:=(Sqrt[x])*Sin[(x^(3/2))+1];
Plot[f[(Sqrt[t])],{t,1,30},AxesLabel->{"t",f[(Sqrt[t])]},PlotStyle->{Red,Thick},GridLines->Automatic]

Remove["Global`*"];
vyr=Integrate[x*Sin[x],{x,1,x}];
f[x_]=vyr;
f[1.2];
(*g[xx_]:=vyr/.x->xx;*)
g[2.]

?f

Remove["Global`*"];

Remove["Global`*"];
ψ=0;
f[t_,ψ_]:={t+Cos[t],Sin[t]}.{{Cos[ψ],Sin[ψ]},{-Sin[ψ],Cos[ψ]}};

ParametricPlot[f[t,ψ],{t,0,2*Pi},AxesLabel->{x,y},PlotStyle->{Magenta,Thick},GridLines->Automatic]

range=8;
Manipulate[

ParametricPlot[f[t,a],{t,0,2*Pi},AxesLabel->{"x","y"},PlotStyle->{Hue[hue],Thickness[tk]},GridLines->Automatic,PlotRange->{{-range,range},{-range,range}}]

,{{a,Pi},0,2Pi},{{tk,0.05},0.001,0.1},{hue,0,1}]

Attributes[Plot]

Remove["Global`*"];
Normal[Series[Tanh[x]+Cos[x],{x,0,5}]];
Plot[Evaluate[Normal[Series[Tanh[x]+Cos[x],{x,0,5}]]],{x,-5,5}]

Remove["Global`*"];
nahr[n_]:=Normal[Series[Sin[1.36*x]+Cos[x],{x,0,n}]];
listNahrad=Table[nahr[n],{n,1,15}];
plot[n_]:=Plot[{Sin[1.36*x]+Cos[x],listNahrad[[n]]},{x,0,2Pi},PlotRange->{Automatic,{-2.5,2.5}},PlotLabel->"n= "<>ToString[n] ,AxesLabel->{"x","f Taylor[f]"},PlotStyle->{{Red,Thick},{Blue,Thick,Dashed}}];
Manipulate[plot[n],{n,1,15,1}]

ClearAll["Global`*"];
(*zaciname obvody*)
R1=4700;
R2=0.12;
L=0.033;
c=4.7*(10^(-6));
f=(1.1/(2*Pi*(Sqrt[L*c])));
uz[t_]:=(10^(-7))*(Exp[19*(1.1Sin[f*2*Pi*t]-0.2)]-1);
Plot[uz[t],{t,0,0.01},PlotRange->All];
rce={0==iR1[t]+iUz[t],
iUz[t]==iC[t]+iR2[t],
iR2[t]==iL[t],
u1[t]==R1*iR1[t],
u2[t]-u3[t]==R2*iR2[t],
u3[t]==L*iL'[t],
iC[t]==c*u2'[t],
uz[t]==u1[t]-u2[t]
};
nezname=Union[Cases[rce,_Symbol[t],{0,∞}]];
poc=Union[Cases[rce,a_'[t]:>a[0]==0,{0,∞}]];
rceDohromady=Union[rce,poc];
tmax=(20/f);
reseni=NDSolve[rceDohromady,nezname,{t,0,tmax}];
Plot[{0.05uz[t],u2[t]/.reseni},{t,0,tmax},PlotRange->All]

rce={uz[t]==ur1[t]+u2[t],
ic[t]==c*D[u2[t],t],
u2[t]==R1*ir11[t],
uz[t]-u2[t]==R1*ir1[t],
ir1[t]==ic[t]+ir11[t]
};
nezname=Union[Cases[rce,_Symbol[t],{0,∞}]];
poc=Union[Cases[rce,a_'[t]:>a[0]==0,{0,∞}]];
rceDohromady=Union[rce,poc];
tmax=(20/f);
reseni=NDSolve[rceDohromady,nezname,{t,0,tmax}];
Plot[{0.05uz[t],u2[t]/.reseni},{t,0,tmax},PlotRange->All]

ClearAll["Global`*"];

R1=100;
R2=200;
R3=300;
L1=0.1;
L2=L1*0.1;
c=10*(10^(-6));
ω=100.*Pi;
Uz=230*(Sqrt[2])*Exp[I*0.2];
Iz=0.1*(Sqrt[2])*Exp[I*(-0.1)];
rce={0==IR2+IR3+IL1,
IR2==IUz,
IR3+Iz==0,
IL1+IC1==Iz+IL2+Iout,
IUz==IR1+IC1,
U5==R1*IR1,
U1-U2==R2*IR2,
U1-U3==R3*IR3,
U5-U4==(1/(ω*I*c))*IC1,
U1-U4==I*ω*L1*IL1,
U4==I*ω*L2*IL2,
Uz==U2-U5
};

neznameAll=Cases[rce,_Symbol,{0,∞}]//Union;
nezname=DeleteCases[neznameAll,Iout];
sol=Solve[rce,nezname][[1]];
Uvystupni=U4/.sol;
Print["Uin= ",Uvystupni/.Iout->0," V,  Zin= ",-D[Uvystupni,Iout]," Ω"]

Length[rce]==Length[nezname];
sol;

Uvystupni

sol=Solve[rce,nezname][[1]];

Uvystupni=U4/.sol;
Print["Uin= ",Uvystupni/.Iout->0," V,  Zin= ",-D[Uvystupni,Iout]," Ω"]

Zin=100.+123.I;
ω=100.Pi;
solRL=Solve[{Re[Zin]==Rin,Im[Zin]==ω*Lin}][[1]];
Print["Rin= ",Rin/.solRL," Ω,  Lin= ",Lin/.solRL," H"]

z1=Rin;
z2=I*ω*Lin;
z=((z1*z2)/(z1+z2));

rceNarh={Re[z]==Re[Zin],Im[z]==Im[Zin]};

solRL=FindRoot[rceNarh,{Rin,100},{Lin,0.1}]
Print["Rin= ",Rin/.solRL," Ω,  Lin= ",Lin/.solRL," H"]

z1=Rin;
z2=I*ω*Lin;
z=((z1*z2)/(z1+z2));

obj={(Re[z]-Re[Zin])^2,(Im[z]-Im[Zin])^2}/.List->Plus

optSol=NMinimize[obj,{Lin,Rin}]

Print["Rin= ",Rin/.optSol[[2]]," Ω,  Lin= ",Lin/.optSol[[2]]," H"]

rceNarh=({Re[z]==Re[Zin],Im[z]==Im[Zin]}//ComplexExpand)//Chop
Solve[%]

ClearAll["Global`*"];
SetDirectory[NotebookDirectory[]];
FileNames[];
data=Import["zarovka2.csv"];
intI=Interpolation[data,InterpolationOrder->1];
{uMin,uMax}=intI[[1,1]];
plotInt=Plot[intI[u],{u,uMin,uMax},PlotLabel->"zarovka 2",PlotStyle->{Red,Thick},GridLines->Automatic,AxesLabel->{"u [V]","i [A]"}];
Show[%,ListPlot[data,PlotStyle->{Black,PointSize[0.02]}]];
model=a*(u^b);
FindFit[data,model,{a,b},u]
proklad=model/.%;
Plot[proklad,{u,uMin,uMax},PlotLabel->"zarovka 2",PlotStyle->{Red,Thick},GridLines->Automatic,AxesLabel->{"u [V]","i [A]"}];
Show[%,ListPlot[data,PlotStyle->{Black,PointSize[0.02]}]]

ClearAll["Global`*"];
par[list_]:=((Total[(list^(-1))])^(-1));
ser[list_]:=Total[list];
R=100;
c1=c2=(10^(-6));
L1=L2=0.1;
za=par[{I*ω*L1,(1/(I*ω*c1))}];
z1=ser[{za,R}];
z2=ser[{I*ω*L2,(1/(I*ω*c2))}];
prenos=(z2/(z1+z2));
LogLogPlot[Abs[prenos],{ω,1,(10^6)},PlotStyle->{Red,Thick},AxesLabel->{"ω [(s^(-1))]","Abs[P] [-]"},GridLines->Automatic,PlotRange->All]
Print["z1[ω=314]= ",z1/.ω->314," Ω"]

ClearAll["Global`*"];
par[list_]:=((Total[(list^(-1))])^(-1));
ser[list_]:=Total[list];
R=100;
c=(10^(-6));
L=0.1;
za=ser[{R,(1/(I*ω*c))}];
zb=par[{R,(1/(I*ω*c))}];
zc=ser[{I*ω*L,zb}];
z1=par[{za,zc}];
zd=ser[{R,I*ω*L}];
ze=par[{zd,R}];
z2=par[{ze,(1/(I*ω*c))}];
prenos=(z2/(z1+z2));
LogLogPlot[Abs[prenos],{ω,1,(10^6)},PlotStyle->{Blue,Thick},AxesLabel->{"ω [(s^(-1))]","Abs[P] [-]"},GridLines->Automatic,PlotRange->All]
Print["z1+z2[ω=1000]= ",z1+z2/.ω->1000," Ω"]

za1=ser[{R,I*w*L}];
za2=par[{(1/(I*w*c)),R}];
za=par[{za1,(1/(I*w*c)),za2}];
z1=ser[{I*w*L,za}];
z2=par[{R,(1/(I*w*c))}];

prenos=(z2/(z1+z2));
LogLogPlot[Abs[prenos],{w,1,(10^6)},PlotStyle->{Blue,Thick},AxesLabel->{"ω [(s^(-1))]","Abs[P] [-]"},GridLines->Automatic,PlotRange->All]
Print["z1+z2[ω=1000]= ",z1+z2/.ω->1000," Ω"]

ClearAll["Global`*"];
rce={b*x+((b^2)-1)*y==1,x-(y/b)==b};
dosZaIkxYpsilon=Solve[rce,{x,y}][[1]];
vysledek=Simplify[(x^2)+(y^2)/.dosZaIkxYpsilon];
Print["(x^2)+(y^2)= ",vysledek];
Plot[vysledek,{b,2,3}]

ClearAll["Global`*"];
f[a_]:=x/.FindRoot[Cos[a*x]==(x^2),{x,-0.1}];
Plot[f[a],{a,0,2}]

(3^(#))-(2^(#))&/@Range[6]

FindSequenceFunction[{1,5,19,65,211,665}][7]