1+1

2+2

%

sin(5)

Sin[5]

Sin[5.]

a=Sin[5];
N[a];
N[a,50];

a=Plot[Sin[(Sqrt[x])],{x,0,1000}];

a

Solve[x^3+ x+1==0,x];
N[%]

(x^2)

Solve[(x^3)+ x+1==0,x];
N[%]

(Sqrt[8])

(56/14)

Solve[(x^3)+ x+1==0,x];

2==3

kyncl je vul

kyncl*je*vul

2jablko

2*jablko

jachym24

?=

a=Random[]

?a

?:=

{a,a,a,a,a}

a:=Random[]

?a

{a,a,a,a,a}

a-a

vyr=(x^(5+Sin[2*(Pi/(Sqrt[2+y]))]))+5y

vyr=(x^(5+Sin[2*(Pi/(Sqrt[2+y]))]))+5y

TreeForm[vyr];

FullForm[vyr]

D[vyr,x]

?___

Sin[Pi]
Sin@Pi
Pi//Sin

Solve[(x^3)==1]//N

Options[Plot]

Plot[Sin[x],{x,0,6Pi},AspectRatio->((.2)/GoldenRatio),ColorFunction->Function[{x,y},ColorData["NeonColors"][y]]]

DSolve[y''[t]+2y'[t]+y[t]==3 Sin[2t],y[t],t]

(*cv 2. - 26.2. 9:15 *)

rovnice={(x^2)+5y+3z==25,((3x)/2)+2y-6z==10,(y/2)-2x+z==1}

Solve[rovnice,{x,y,z}]//N

x->(216/287)//FullForm

a==b//FullForm

?/.

x/.x->2

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

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

{1,2,5}[[1]]

rce={x+y==5,x-y==1};
sol=Solve[rce]
(x^2)+2(y^2)/.sol
(x^2)+2(y^2)/.sol[[1]]

x+y==5/.Equal->List

x+y==5//FullForm

List[Plus[x,y],5]

a+b+c+d//FullForm

List[a,b,c,d]

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

{a,b,c,d}/.List->Plus

Solve[eqn]

eqn=(∑_(i=0)^17)1.*((x^i)/(i!))==0;
abshodnoty=Abs[x]/.Solve[eqn]
abshodnoty/.List->Plus

Abs[x]/.{{x->-1},{x->-2}}

{a,b,c,d}/.List->Plus

ClearAll[x]
a=3;
sol=FindRoot[Cos[a*x]==x,{x,0}]
vysledek=x/.sol
(*sol[[1,2]]*)

sol//TreeForm;

ClearAll[reseni];
reseni[a_]:=x/.FindRoot[Cos[a*x]==x,{x,0}];
reseni[3]

x/.{x->blabla}

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

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

ClearAll[f]
f[a_]:=Max[Abs[x]/.Solve[a*(x^2)+x+1==0.,x]];
Plot[f[a],{a,1,10}]

ClearAll[f]
f[a_]:=Sin[a+x]/.FindRoot[(E^(a*x))==-a*x,{x,0}]

Plot[f[a],{a,2,3},AxesLabel->{"osa X","osa Y"},PlotStyle->{Red,Thick}]

(*zde zacina treti cviko*)
n=1;
hue=0.5;
ParametricPlot[{Sin[n*x],Cos[x]},{x,0,2Pi},AxesLabel->{"osa X","osa Y"},PlotStyle->{Hue[hue],Thick}]

Manipulate[

ParametricPlot[{Sin[n*x],Cos[x]},{x,0,2Pi},AxesLabel->{"osa X","osa Y"},PlotStyle->{Hue[hue1],Thick}]

,{n,1,5,1},{{hue1,0.5},0,1}]

Table["opice",{12}]

Table[(i^2),{i,12}]

Table[i,{i,0,12,0.7}]

mat=Table[(E^i)+(Pi^j),{i,4},{j,4}];

MatrixForm[mat];

Det[mat]

ClearAll[n]

Fit[{{1,0},{11,1}},{1,n},n]

plot[hue_,n_]:=Plot[(x^n),{x,-1.2,1.2},AxesLabel->{"osa X","osa Y"},PlotStyle->{Hue[hue],Thickness[0.006]},PlotRange->{{-1,1},{-1,1}}];

Grafy=Table[plot[((n-1)/10),n],{n,1,11,2}];
vysledek=Show[Grafy];
SetDirectory[NotebookDirectory[]];
Export["graf1.png",vysledek,ImageResolution->300]

Range[10]

{1,2,3,4,5,6,7,8,9,10}[[6]]

Rteor=27;
rnU:=RandomReal[{-0.1,0.1}];
rnI:=RandomReal[{-0.01,0.01}];
dataU=Table[Rteor*i+rnU,{i,1,5,0.1}];
dataI=Table[i+rnI,{i,1,5,0.1}];
nmax=Length[dataU]

Table[((dataU[[i]])/(dataI[[i]])),{i,1,Length[dataU]}];
Mean[%]

{dataU,dataI}\[Transpose];

Transpose[{dataU,dataI}]/.{u_,i_}:>(u/i);
Mean[%]

Thread[{dataU,dataI}]/.{u_,i_}:>(u/i);
Mean[%]

(dataU/dataI);
Mean[%]

(({a,b,c})/({d,e,f}))

(*Off[Solve::ifun]*)

rce=y'[x]+2*Sin[y[x]]==0;
DSolve[rce,y[x],x]

(* Zde zacina ctvrte cviko 12.3.2018 *)

R1=100;
R2=100;
c=4.7*(10^(-6));
L=0.01;
Uz=10*Sin[1000Pi*t];
IIz=0.01;
RceUzly={IIz+IU[t]==IR2[t]+Ic[t],IR2[t]==IU[t]+IR1[t],IR1[t]==IL[t]};
RceSouc={IR2[t]*R2==U1[t]-U2[t],U1[t]-U2[t]==Uz,U2[t]-U3[t]==R1*IR1[t],U3[t]==L*D[IL[t],t],Ic[t]==c*D[Uc[t],t],Uc[t]==U1[t]};
pom=Union[RceSouc,RceUzly];
nezname=Cases[pom,_Symbol[t],{0,∞}]//Union;
{Length[pom],Length[nezname]};
poc=Cases[pom,a_'[t]:>a[0]==0,{0,∞}]//Union;
dohr=Union[pom,poc];
tmax=0.01;
sol=NDSolve[dohr,nezname,{t,0,tmax},StartingStepSize->(10^(-9))];
Plot[Uc[t]/.sol,{t,0,tmax}]

ClearAll["Global`*"]

R1=100;
R2=200;
c=0.001;
L=0.2;
Iz=10*Sin[314*t+0.1];
Uz=150*Sin[314*t];

Uzly={IUz[t]==IL[t]+IR1[t],IR2[t]==IL[t]+Iz,IR1[t]==Iz+IC[t]};

Souc={Uz==-U1[t],U2[t]==R2*IR2[t],U1[t]-U3[t]==R1*IR1[t],U1[t]-U2[t]==L*D[IL[t],t],IC[t]==c*D[UC[t],t],UC[t]==U3[t]};

pom=Union[Uzly,Souc];
nezname=Cases[pom,_Symbol[t],{0,∞}]//Union;
{Length[pom],Length[nezname]};
poc=Cases[pom,a_'[t]:>a[0]==0,{0,∞}]//Union;
dohr=Union[pom,poc];
tmax=0.2;

res=NDSolve[dohr,nezname,{t,0,tmax},StartingStepSize->(10^(-15)),Method->{"IndexReduction"->Automatic},MaxSteps->(10^7)];

Plot[IC[t]/.res,{t,0,tmax}]