a=(x^2)+Sin[3x+5]+1+1+2α

FullForm[a]

a=(x^2)+Sin[3x+5]+1+1+2α

TreeForm[a]

TreeForm[b+3]

b+3=5

?_

?__

?___

N[Pi]

N[Pi,100]

ClearAll[f];
f[x]:=(x^2);
f[x]
?f

?:=

?=

ClearAll[f];
x=123;
f[x:_]:=(x^2)
f[5]
?f

ClearAll[f];
f[x:_]:=∫Sin[x]\[DifferentialD]x;
f[5]

ClearAll[f,x];
f[x:_]=∫Sin[x]\[DifferentialD]x
f[5]

ClearAll[f];
f[x_]:=(x^2);
f[0.4]

ClearAll[f];
f[x_]:=(x^2);
f[x_,y_]:=(x^y);
f[1]:=5;
f[x_,4]:="opice";
f[{a_,b_}]:={b,a};
f[{1,2}]

$RecursionLimit=(10^6);
ClearAll[a];
a[n_]:=n*a[n-1];
a[0]:=1;
Timing[Table[a[i],{i,1000}]][[1]]
?a

Timing[Table[a[i],{i,800}]][[1]]

Trace[a[4]]

ClearAll[a];
a[n_]:=a[n]=n*a[n-1];
a[0]:=1;
Timing[Table[a[i],{i,20}]][[1]]
Trace[a[21]]

listik={1,2,3}

TreeForm[listik]

listik=(({{12, 3}, {2, 3}, {5, 7}}))

TreeForm[listik]

listik={ja,{alfa,romeo},{{3}}};
listik[[1]]
Part[listik,1]

listik={ja,{alfa,romeo},{{3}}};
listik[[1]]
First[listik]

listik={ja,{alfa,romeo},{{3}}};
listik[[-1]]
Last[listik]

listik={ja,{alfa,romeo},{{3}}};
listik[[2]][[2]]
listik[[2,2]]

listik[[0]]
Head[listik]

Table["opice",{12}]

Table[(i^3),{i,10}]

Table[i,{i,0.5,10,0.4}]

(*zde zacina druhy prednes*)

Evaluate[Context[]<>"*"]

Sin[5]
5//Sin
Sin@5

Quiet@Remove["Global`*"]
SetDirectory[NotebookDirectory[]]
$HistoryLength=3;
FileNames[]

Solve[(x^2)==a,x]

Solve[{x+y==1,x-y==2},{x,y}]

Solve[x==a,x]

Quiet@Remove["Global`*"]
c=Equal[a,b]

a=1;
b=1;
c

?===

?==

?/.

(x^2)/.{x->5,x->6}

dos=Solve[(x-5)*(x-6)==0]
x1=x/.dos[[1]];
x2=x/.dos[[2]];
x1+(x2^2)

dos[[1,1,2]]+((dos[[2,1,2]])^2)

x->5//TreeForm

(x^2)/.{{x->5},{x->6}}

Series[Cos[x],{x,0,10}]

rce=Cos[x]==x;
TreeForm@rce;
dosadZaIks=FindRoot[rce,{x,0}]
(rce/.a_==b_:>a-b)/.dosadZaIks

{a,b}

rce/.a_==b_->a-b

list=Range[10]

list/.List->Times

list=Range[10];
test[x_]:=x<6;
Select[list,test]

naDruhou[x_]:=(x^2);
naDruhou[5]

((#)^2)&[5]

Plot3D[#1+((#2)^2)&[x,y],{x,-2,2},{y,-2,2}]

ggg=#1+((#2)^2)&;
ggg[Pi,E]

Select[list,#<6&]

Sin/@Range[100]

listik={ja,ty,on,ona,ono};
Map[ostrihejVlasy,listik];
ostrihejVlasy/@listik;

natocPecko/@listik;

Apply[natocPecko,pom=Drop[listik,-1]]
natocPecko@@pom

TreeForm/@{pom,natocPecko@@pom}

Plus@@pom

TreeForm/@{pom,Plus@@pom}

tmax=2;
nKroku=20;
tStart=0.;
y0=1;
pocatecniBod={tStart,y0};
Δt=((tmax-tStart)/nKroku);
krok[{t_,y_}]:={t+Δt,y+(-2y)*Δt};
res=NestList[krok,pocatecniBod,nKroku];
ListPlot[res]

NestList[f,x0,5]

Nest[f,x0,5]

(*zde zacina treti prednes*)
Quiet@Remove["Global`*"]

R1=R2=R3=R4=R5=R6=100;
uz=10;
iuz=0.01;
rceUzlu={iuz==iR1+iR2,
iR3+iR6==iz+iuz,
iR4==iR6+iR5+ivyst,
iR2==iR3+iR4
};
rceSoucastek={u1==R1*iR1,
u1-u4==R2*iR2,
u4-u2==R3*iR3,
u4-u3==R4*iR4,
u3==R5*iR5,
u3-u2==R6*iR6,
uz==u1-u2
};
rceDohr=Union[rceUzlu,rceSoucastek];
proms=Union[Cases[rceDohr,_Symbol,{0,∞}]]
{Length[proms],Length[rceDohr]}

rceIvystRovnoNule=rceDohr/.ivyst->0;
Solve[rceIvystRovnoNule]

nezname=DeleteCases[proms,ivyst];
Solve[rceDohr,nezname]

Quiet@Remove["Global`*"];
ser[list_List]:=Total[list];
ser[{R1,R2,R3}];
par[list_List]:=((Total[(list^(-1))])^(-1));
par[{R1,R2,R3}];

Ra=ser[{R2,R4}];
Rb=par[{Ra,R3}];
Rc=par[{R6,R5}];
Rd=ser[{Rc,Rb}];
Rvysl=par[{Rd,R1}]//Simplify

(*zde zacina ctvrta prednaska*)
Quiet@Remove["Global`*"]
uz[t_]:=Tanh[10*Sin[2*Pi*50*t+1.12321]];
tmax=0.08;
Plot[uz[t],{t,0,tmax}];
R=100;
c=3.65*(10^(-9));
L=0.001;
rce={iU[t]==iR[t],
iR[t]==iC[t],
iC[t]==iL[t],
u1[t]-u2[t]==R*iR[t],
iC[t]==c*D[u2[t]-u3[t],t],
u3[t]==L*iL'[t],
uz[t]==u1[t]
};
pocPodm=Cases[rce,a_'[t]:>a[0]==0,{0,∞}];
nezname=Union[Cases[rce,_Symbol[t],{0,∞}]];
{Length[rce],Length[nezname]};
NDSolve[Union[rce,pocPodm],nezname,{t,0,tmax}]

Head/@rce

Quiet@Remove["Global`*"]
uz[t_]:=Tanh[10*Sin[2*Pi*50*t+1.12321]];
tmax=0.08;
Plot[uz[t],{t,0,tmax}];
R=100;
c=3.65*(10^(-6));
L=0.1;
rce={iU[t]==iR[t],
iR[t]==iC[t],
iC[t]==iL[t],
u1[t]-u2[t]==R*iR[t],
uC[t]==u2[t]-u3[t],
iC[t]==c*uC'[t],
u3[t]==L*iL'[t],
uz[t]==u1[t]
};
pocPodm=Cases[rce,a_'[t]:>a[0]==0,{0,∞}];
nezname=Union[Cases[rce,_Symbol[t],{0,∞}]];
{Length[rce],Length[nezname]};
res=NDSolve[Union[rce,pocPodm],nezname,{t,0,tmax},StartingStepSize->(10^(-9)),MaxSteps->(10^6)];
rnu3=0.00005;
Plot[u3[t]/.res,{t,0,tmax},PlotRange->{Automatic,{-rnu3,rnu3}}];
Plot[u3[t]/.res,{t,0,tmax}]

Quiet@Remove["Global`*"]
uz[t_]:=10*Sin[2*Pi*50*t+1.12321];
tmax=0.08;
Plot[uz[t],{t,0,tmax}];
R=100;
c=3.65*(10^(-6));
L=0.1;
rce={iU[t]==iR[t],
iR[t]==iC[t],
iC[t]==iL[t],
u1[t]-u2[t]==R*iR[t],
uC[t]==u2[t]-u3[t],
iC[t]==c*uC'[t],
u3[t]==L*iL'[t],
uz[t]==u1[t]
};
pocPodm=Cases[rce,a_'[t]:>a[0]==0,{0,∞}];
nezname=Union[Cases[rce,_Symbol[t],{0,∞}]];
{Length[rce],Length[nezname]};
res=NDSolve[Union[rce,pocPodm],nezname,{t,0,tmax},StartingStepSize->(10^(-9)),MaxSteps->(10^6)];
rnu3=0.00005;
Plot[u3[t]/.res,{t,0,tmax},PlotRange->{Automatic,{-rnu3,rnu3}}];
Plot[u3[t]/.res,{t,0,tmax}]

FullForm[u3[t]/.res];

z=3+4I;
{Re[z],Im[z],Abs[z],Arg[z],z==Abs[z]*Exp[I*Arg[z]]}

Plot[Im[10*(2+3I)*(E^(I*2*Pi*50*t))],{t,0,0.02}]

ω=314.;
Um=10.56;
fi=0.562;
Ufazor=Um*Exp[I*fi]
u[t_]:=Im[Ufazor*Exp[I*ω*t]];
Plot[u[t]-Um*Sin[ω*t+fi],{t,0,0.02}]

(*Zde zacina paty tyden*)

Series[y[t+Δt],{Δt,0,5}]

Quiet@Remove["Global`*"]

Nest[f,x0,5]

NestList[f,x0,5]

{EvenQ[1],EvenQ[2]}

NestWhileList[#/2&,123456,EvenQ]

vydelDvema[x_]:=(x/2);
NestWhileList[vydelDvema,123456,EvenQ]

DSolve[y'[t]==(((t+1)*Log[y[t]+1])/(((y[t])^2)+t*y[t]+1)),y[t],t]

krokEuler[pocatecniStav]

ClearAll[derivace,krokEuler]
derivace[{t_,y_}]:=(((t+1)*Log[y+1])/((y^2)+t*y+1));
tStart=0.;
tEnd=10;
nKroku=500;
yStart=1;
Δt=((tEnd-tStart)/nKroku);
krokEuler[stav:{t_,y_}]:={t+Δt,y+Δt*derivace[stav]};
pocatecniStav={tStart,yStart};
reseni=NestList[krokEuler,pocatecniStav,nKroku];
ListPlot[reseni]

λ[x_]:=0.04+(1+Tanh[(x-0.1)*10000])*0.5*(0.8-0.04);
Plot[λ[x],{x,0,0.6},PlotRange->All,PlotStyle->Thick];
Plot[λ'[x],{x,0,0.6},PlotRange->All,PlotStyle->Thick];
D[λ1[x]*D[T[x],x],x]==0;
eqn=D[λ[x]*D[T[x],x],x]==0;
res=NDSolve[{eqn,T[0]==-10,T[0.5]==20},T,{x,0,0.5},MaxStepSize->(10^(-3))];
Plot[T[x]/.res,{x,0,0.6},PlotRange->All,PlotStyle->Thick]

Options[NDSolve]