1+1

(Sqrt[5])

(Sqrt[5.])

N[(Sqrt[5])]

n[(Sqrt[5])]

N[Pi,50]

Sin[5]
Sin@5
5//Sin

123!//N

LaplaceTransform[t*(E^(-2t))Sin[π*t],t,p]

?*Lapla*

InverseLaplaceTransform[(((p^2)+a)/((p^2)-5p+6)),p,t]

kyncl je idiot

kyncl*je* idiot

12opice

opice12

Integrate[(x^2)*(E^(-(x^2))),x]

DSolve[y''[x]-5y'[x]+6y[x]== Sin[3x],y[x],x]

1==2

1=2

a=2

?:=

ClearAll[a]

x=4;

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

x=4;
ClearAll[f,x]
f[x_]=(x^2);
?f

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

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

ClearAll[g](*komentar*)
g[x_,y_]:=(π^x)+(y^E);
g[x_]:="opice";
g[0]:="slepice";
g[x_Integer]:="lachtan";
g[x_,8]:="nebij me";
g[x_Integer,8]:="bij me";

g[5,8]

g[osel]
g[5]
g[0]

ClearAll[a];
a[n_]:=n*a[n-1]
a[0]:=1;

Trace[a[3]]

ClearAll[a];
a[n_]:=a[n]=n*a[n-1];
a[0]:=1;

a[5]

?a

ClearAll[a]

1.[[0]]

mujlist={a,b,c,{d,e}};
mujlist[[4,2]]
mujlist[[0]]
(*mujlist//TreeForm*)

TreeForm[mujlist]

(x^2)+Sin[3+(E^x)]//TreeForm;

ClearAll[x]
(x^2)+Sin[3+(E^x)]//Speak

(*druhe sezeni*)

Table[opice,{12}]

Table[(x^i),{i,9.5}]

Table[(x^i),{i,2,3.5}]

Table[(x^i),{i,2,3.5,0.5}]

table=Table[(Pi^i)+(j^E),{i,3},{j,3}]
mfTable=%//MatrixForm

table=Table[(Pi^i)+(j^E),{i,3},{j,3}]
mfTable=MatrixForm[table]

Grid[table,Frame->All]

?Plot

??Plot

"y"[[0]]

"1"+"2"

$HistoryLength=2;

x=20!;
mujplot=Plot[{Sin[x],Cos[0.5x]},{x,0,6Pi},AxesLabel->{"x","Sin[x] Cos[0.5x]"},PlotLabel->"prvni grafik",PlotStyle->{{Thick,Green,Dashed},{Red,Thick}},GridLines->Automatic];

SetDirectory[NotebookDirectory[]];

(*Export["dalkarskyplot.tiff",mujplot,ImageResolution->300]*)

Plot[Sin'[x],{x,0,6}];

ClearAll[x]
D[Sin[x],x]

D[(y^2)+Sin[x*Cos[x+y]],x,y,x];

Plot[Integrate[Sin[x],x],{x,0,6}]

Plot[Evaluate[Integrate[Sin[x],x]],{x,0,6}]

Plot[Evaluate[D[Sin[x],x]],{x,0,6}]

Plot[D[Sin[x],x],{x,0,6}]

man=Manipulate[
aaa=(Sqrt[a+(b^2)]);

Plot[{aaa*Sin[x],b*Cos[a*x]},{x,0,6Pi},AxesLabel->{"x","Sin[x] Cos[0.5x]"},PlotLabel->"aaa= "<>ToString[aaa],PlotStyle->{{Thick,Green,Dashed},{Red,Thick}},GridLines->Automatic]

,{{a,0.5},0,1,0.1},{b,0.2,0.8}];

(*Export["tst.swf",man]*)

test[x_]:=x>2;
Select[{1,2,4,7,6,2},test]

((#)^2)&[5]

ff[x_,y_]:=x+(y^2);
ff[Pi,E]

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

Sin'

Plot[((#)^2)&[x],{x,-1,1}]

ClearAll[f];
f[a_]:=Sin[a*#]&;
f[3][x]

(*treti sezeni*)

Solve[2x+3==5.]

?/.

2(x^2)+3/.x->5

2(x^2)+3/.{x->5}

2(x^2)+3/.{{x->5}}

2(x^2)+3/.{{x->5},{x->a}}

{53,3+2 (osel^2)}

dosadzax=Solve[(1+(a^2))(x^2)+(1-(a^2)) x+a==0,x];

protisk=((1+(x^2))/a)/.dosadzax[[2]]

Plot[protisk,{a,1,10},AxesLabel->{"a","f[a]"},PlotStyle->{Red, Thick}]

FindRoot[Cos[2x]==0.5x,{x,0}]

Sin[2x-1]/.FindRoot[Cos[2x]==0.5x,{x,0}]

a=osel;
b=selka;

Cos[2x]==0.5x/.a_==b_->a-b

Cos[2x]==0.5x/.a_==b_:>a-b
%/.FindRoot[Cos[2x]==0.5x,{x,0}]

rce=(∑_(i=1)^50)((x^i)/(i!))==0//N;
koreny=x/.Solve[rce];
koreny/.List->Plus

5.==5

(x^2)+Sin[5t]/.{Sin->Cos,5->7,Plus->Times,2->3,x->t}

DSolve[f'[x]==f[x]Cos[f[x]],f[x],x]

(*NSolve
DSolve*)
vysledek=NDSolve[{f'[x]==f[x]Cos[f[x]],f[0]==1},f,{x,0,30}];
Plot[f[x]/.vysledek[[1]],{x,0,30},PlotStyle->Thick,PlotRange->All]

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

230.*(Sqrt[2])

(* 4 prednaska*)

R1=10;
R2=1000;
R3=15;
L=1;
c=10*(10^(-9));

Uz=230*Tanh[50*Sin[2*Pi*50*t]];
Iz=10*Sin[2*Pi*50*t];

Plot[Uz,{t,0,0.04},PlotStyle->Thick];

rceUzly={Iuz[t]==IR3[t],IR3[t]==IL[t]+IC[t]+IR2[t],Iz+IL[t]+IC[t]==0,0==Iz+IR1[t]};
rceSoucastky={U1[t]-U2[t]==R3*IR3[t],U2[t]-0==R2*IR2[t],U4[t]-0==R1*IR1[t],Uc[t]==U2[t]-U3[t],IC[t]==c*Uc'[t],U2[t]-U3[t]==L*IL'[t],Uz==0-U1[t]};
pocPodminky={Uc[0]==0,IL[0]==0};

vsechnyRce=Union[rceUzly,rceSoucastky,pocPodminky];
vsechnyNezname=Union[Cases[vsechnyRce,_Symbol[t],Infinity]];
reseni=NDSolve[vsechnyRce,vsechnyNezname,{t,0,0.04},StartingStepSize->(10^(-12)),MaxSteps->(10^5)][[1]];

Plot[{Uz,U3[t]/.reseni},{t,0,0.04},PlotRange->All]

TreeForm[vsechnyRce];

(1/(2.*Pi(Sqrt[L*c])))

FullForm[reseni]