1+1

a=3;
b=2;
a+b

Sin[π]
π//Sin
Sin@π

Sin[5]

Cos[((7π)/8)]

(Sqrt[8])

N[(Sqrt[8])]

N[(Sqrt[8]),40]

(Sqrt[8.])

vyr=(x^2)*Sin[(1/(Tan[4-((Sqrt[x])+1)]))]

TreeForm[vyr]
FullForm[vyr]

Plot[vyr,{x,0,6Pi}]

LaplaceTransform[(t^3)Sin[10t+0.4],t,p]

Plot[(x^2),{x,0,6Pi}];

listik={1,{"osel","volek"},{{-1,3}}}

listik[[2,-1]]

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

listik[[0]]

TreeForm[listik]

listik[[2]][[1]]
listik[[2,1]]

x=kyncl je vul

opice=5

12opice

x=2

Solve[(x^2)+2==1]

ClearAll[x]
Solve[(x^2)+2==1]

ClearAll[x]

x*2

2x

opice12

Blue

Options[Plot]

Plot[{Cos[x],Sin[x]},{x,0,6Pi},AxesLabel->{"x","sin(x) , cos(x)"},PlotStyle->{{Red,Thick,Dashing[{0.01,0.02,0.03}]},{RGBColor[0,0,1],Dashed,Thickness[0.001]}}]

Plot[Tan[x],{x,0,6Pi},PlotRange->All]

Plot[Tan[x],{x,0,6Pi},PlotRange->{{0,5},{-10,10}}]

Plot[Tan[x],{x,0,6Pi},PlotRange->{Automatic,{-10,10}}]

?_

ClearAll[f];
f[0]:=1;
f[x:_]:=(x^2);

ClearAll[f];
f[0]:=1;
f[x_]:=(x^2);
f[x_,y_]:=(x^y);
f[x_,2]:=3+x;
f[{x_,y_}]:={x-y};
f[{x_,y_Integer}]:="dej pokoj!!!";

f[0,2]

?:=

?=

ClearAll[f];
f[x_]:=Integrate[Sin[x],x]

f[4]
?f

ClearAll[f];
f[x_]=Integrate[Sin[x],x]

f[4]
?f

a:=Random[]
?a
{a,a,a,a,a,a,a}

a=Random[]
?a
{a,a,a,a,a,a,a}

ClearAll[f];
f[x_]:=Module[{a,b,c,d=0.4},
a=(x^0.2);
b=(((a+x))^(x-d));
c+b+a
];
f[-1]

ClearAll[a];
a[n_]:=n*a[n-1];
a[0]:=1;
a[3]

Trace[a[3]];

a/@Range[6]
FindSequenceFunction[%,n]

Table["dalmatin",{101}];

Table[i,{i,12.2}]

Table[i,{i,0,6.2,0.3}]

mat=Table[(E^i)+(Pi^j),{i,4},{j,4}];
MatrixForm[mat];
Grid[mat,Frame->All];

$RecursionLimit=(10^6);

ClearAll[a];
a[n_]:=n*a[n-1];
a[0]:=1;
Timing[Table[a[i],{i,3000}]][[1]]

ClearAll[a];
a[n_]:=a[n]=n*a[n-1];
a[0]:=1;
Timing[Table[a[i],{i,3000}]][[1]]

derivace[{t_,y_}]:=-y;
pocBod={0,1};
tmax=4;
nKroku=20;
Δt=(tmax/nKroku);
krok[bod:{t_,y_}]:=bod+{Δt,Δt*derivace[bod]};
NestList[krok,pocBod,nKroku];

NestList[f,x0,10];

NestList[Cos,0.,20]//ListPlot;

derivace[{t_,y_}]:=-y;
pocBod={0.,1.};
tmax=4;
nKroku=120;
Δt=(tmax/nKroku);
krok[bod:{t_,y_}]:=bod+{Δt,Δt*derivace[bod]};
res=NestList[krok,pocBod,nKroku];
ListPlot[res]

n=2;
rce=0==(∑_(i=0)^n)(x^i)*(Subscript[a, i])
Solve[rce,x]

?/.

sekyra+topurko/.{sekyra->2zlaty,topurko->tolar}

(x^4)+5y/.x->2t

1==2

2==2

FullForm[g==h]

res

rce=(1+(t^2))*(x^2)+Cos[t]*x+Sin[t]==0;
res=Solve[rce,x];
x1=x/.res[[1]];
x2=x/.res[[2]];
Plot[Abs[x1]+Abs[x2],{t,-20,20},PlotRange->All]

y[0]

ClearAll[y]
res=DSolve[{y'[x]+y[x]==1 Sin[x],y[0]==0},y[x],x]
protisk=y[x]/.res[[1]]
Plot[protisk,{x,0,50}]

Quiet@Remove[Evaluate[Context[]<>"*"]]

list=Range[10]

Map[f,list]
f/@list

Apply[f,list]
f@@list

list//TreeForm;

Apply[f,list]//TreeForm;

Plus@@list

Attributes[Sin]

Sin[list]

ClearAll[f]
f[list]
f/@list

ClearAll[f]
SetAttributes[f,Listable]
f[list]

ClearAll[par,ser];
par[list_]:=(((Plus@@((list^(-1)))))^(-1));
ser[list_]:=Plus@@list;
par[{r1,r2,r3}];
ser[{r1,r2,r3}];

za=ser[{R1,I*ω*L1}];
zb=par[{za,(1/(I*ω*C1))}];
z1=ser[{zb,I*ω*L2,(1/(I*ω*C2))}];
zc=ser[{R2,I*ω*L3}];
z2=par[{zc,(1/(I*ω*C3))}];
prenos=(z2/(z1+z2));
dosad={R1->1,L1->0.05,C1->1.5*(10^(-6)),C2->0.1*(10^(-6)),C3->1.5*(10^(-9)),L2->0.01,L3->0.005,R2->1};
prenosCiselne=Simplify[prenos/.dosad];
LogLogPlot[Abs[prenosCiselne],{ω,0.1,(10^9)},AxesLabel->{"ω [(s^(-1))]","Abs[P] [-]"},PlotRange->All,GridLines->Automatic]

LogLinearPlot[20Log[10,Abs[prenosCiselne]],{ω,0.1,(10^9)},AxesLabel->{"ω [(s^(-1))]","Abs[P] [dB]"},PlotRange->All,GridLines->Automatic]

LogLinearPlot[Arg[prenosCiselne],{ω,0.1,(10^8)},AxesLabel->{"ω [(s^(-1))]","Abs[P] [dB]"},PlotRange->All,GridLines->Automatic]

z=3+4I;
{Re[z],Im[z],Abs[z],Arg[z],Abs[z]*(E^(I*Arg[z]))}//N