1+1

a=1
β=d

Sin[4]

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

Sin[4.]

N[Sin[4],100]
Sin[4]//N

Pi

π

lubos=3;

franta=5;

ClearAll[lubos]

Pi=3

DSolve[x''[t]+5x'[t]+4x[t]== ((Sin[Cos[t]])/(E^t)),x[t],t]

DSolve[x''[t]+5x'[t]+4x[t]==((Sin[Cos[t]])/(E^t)),x[t],t]

DSolve[{x'[t]==Sin[t],x[0]==1},x[t],t]

Solve[{x+y==4, 3x-y==4},{x,y}]

{x+y==4, 3x-y==4}//TreeForm

list={{a,b},{c,d},e};

list[[1]]

list[[2]]

list[[1,2]]

list[[-1]]==list[[3]]

rce=Sin[x]==0;

Solve[rce,x]

FindRoot[rce,{x,1}]

FindRoot[rce,{x,2}]

Plot[{2,Sin[x],Log[x],(E^(-x))},{x,0,10},PlotStyle->{{Blue,Dashed},{Red},{Purple,Thick},{Orange,Dotted}},AxesLabel->{"osa x","osa y"}]

(*Zde začíná druhé cviko*)

resUkol=Solve[{a+b==k,(a^2)-b==2},{a,b}]

a/.a->3

a+b/.{a->3,b->2}

a/.{a->2,a->3}

res=Solve[a*(x^2)+b*x+c==0,x]

x/.res[[2]]

proPlot1res={a,b}/.resUkol[[1]]

proPlot2res={a,b}/.resUkol[[2]]

gr1=Plot[proPlot1res,{k,0,5}]

gr2=Plot[proPlot2res,{k,0,5}]

Show[gr1,gr2]

proPlot3=Union[proPlot1res,proPlot2res]

Union[{a,b,c,d},{b,c,e,f}]

xxx=3;
Plot[proPlot3,{k,0,5},AxesLabel->{"xxx","yyy"},PlotLabel->"Graph",PlotStyle->{{Thick,RGBColor[0,1,0.5]},{Thick,Blue},{Thick,Dashed},{Hue[0.25],Dashed}}]

Manipulate[Graphics[{Hue[k],Disk[]}],{k,0,1,0.002}]

Manipulate[Graphics[{RGBColor[red,green,blue],Rectangle[]}],{red,0,1,0.002},{green,0,1,0.002},{blue,0,1,0.002}]

Manipulate[Plot[A*Sin[2Pi*f*t+fi]+str,{t,-0.01,0.04},PlotRange->{Automatic,{-1,1}}],{A,0,1},{f,50,100,10},{fi,0,2Pi},{str,-2,2}]

Table[{i,(i^2),(i^3),(Sqrt[i]),i},{i,1,100,5}];

proListPlot=Table[{i,(i^2)},{i,-5,5,0.1}];
ListPlot[proListPlot,AxesLabel->{"xxx","yyy"},PlotLabel->"Graph",PlotStyle->{PointSize[0.05],Green},Joined->True]

proListPlot=Table[{i,(i^2)+Random[Real,{-5,5}]},{i,-5,5,0.1}];
ListPlot[proListPlot,AxesLabel->{"xxx","yyy"},PlotLabel->"Graph",PlotStyle->{PointSize[0.01],Green}]

(*zde zacina 3. cviceni*)

rce={y'''[t]+4y''[t]+2y'[t]-y[t]==4(E^(-3t)),y[0]==1,y'[0]==4,y''[0]==2};

res=y[t]/.DSolve[rce,y[t],t][[1]]

Plot[res,{t,0,100},PlotLabel->"graf",AxesLabel->{"t","y"},PlotStyle->{Green,Thick},PlotRange->All]

polynom[{k_}]:=0==Plus@@Table[(Subscript[a, i])*(x^i),{i,0,k}]

Solve[polynom[{1}],x]

polynom2[k_]:=Module[{polnom,res},
polnom=0==Plus@@Table[(Subscript[a, i])*(x^i),{i,0,k}];
res=Solve[polnom,x];
x/.res
]

polynom2[6]

rce={UA[t]==U,((UA[t]-UB[t])/R)==kap*D[UB[t],t],UB[0]==0}/.{U->5,R->1,kap->10*(10^(-3))};
res=DSolve[rce,{UB[t],UA[t]},t];
Plot[{UA[t]/.res,UB[t]/.res},{t,0,.1},PlotRange->All]