1+1

BaseForm[2,2]

PrimePi[2]

Sin[3]

sin[3]

(Sqrt[2])

(Sqrt[2.])

46.*(Sqrt[2])

N[(Sqrt[2])]

N[(Sqrt[2]),50]

N[(Sqrt[3])]

Solve

(Sqrt[\[Placeholder]])

(2^3)

(a/(b
((a+b)/(c+d
))))

∫(E^x)*Sin[x]*Cos[x]*x\[DifferentialD]x

fel=3

fel

Clear[fel]

Clear[Sin]

I=5

∫(E^x)*Sin[x]*Cos[x]*x\[DifferentialD]x

Plot[(1/50) (E^x) ((4-10 x) Cos[2 x]+(3+5 x) Sin[2 x]),{x,-18.42477796076938`,18.42477796076938`}]

A=5;
B=2;

Solve[A*x+B==10,x]

A=5;
B=N[2];

Solve[A*x+B==10,x]

(((a+b)*(c+9d))/(3*(2+(1+x*(3+1)))))

{A,B}

TreeForm[{1,3,2,4,5,{2,5,4,8}}]

Solve[{2*x+y==2,3*x-6==y},{x,y}]

Solve[{2*x+y==2,3*x-6==y},{x,y}]

Clear[x]
Solve[x==2,x]

DSolve[{(1+(x^2))*y''[x]+x*y'[x]+y[x]==0,y[0]==3,y'[0]==2},y[x],x]

DSolve[{(1+(x^2))y''[x]+x*y'[x]+y[x]==0,y[0]==3,y'[0]==2},y,x]

2 3

10vez

vez10=25

vez10

N[Pi]
N[E]
N[Log[3]]

cosfi=0.4;

fi=ArcCos[cosfi];
Sin[fi]

N[(Sqrt[2])]

(Sqrt[2])//N

N@(Sqrt[2])

(*zde zacina druhe cviceni 29.2.2016*)

Solve[{(x^2)+x*y+c==20,y+10*y*c+15*x==8},{x,y}]

Solve[{(x^2)+x*y+c==20,y+10*y*c+15*x==8},{x,y}]

Plot[(-4-(Sqrt[2]) √(-132-1293 c+1065 (c^2)-50 (c^3)))/(2 (-7+5 c)),{c,-5,5}]

{1,2,3,5,{1,8,4},1}[[5,2]]

res=Solve[{(x^2)+x*y+c==20,y+10*y*c+15*x==8},{x,y}];

res[[3]]

x/.{x->1}

y/.{x->1}

Solve[(x^2)+3*x+1==0,x]

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

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

x

x1=x/.res[[1]];(* koren x1*)
x2=x/.res[[2]];(* koren x2*)
y1=y/.res[[1]];(* koren y1*)
y2=y/.res[[2]];(* koren y2*)

z=3
Plot[{x1,x2,y1,y2},{c,-5,5},PlotStyle->{{Red,Thick,DotDashed},{Green,Dashed,Thick},Hue[0.6],RGBColor[0.7,0.15,0.6]},AxesLabel->{"c","x1,x2,y1,y2"},PlotLegends->{"x1","x2","y1","y2"},PlotRange->{Automatic,{-5,10}},PlotLabel->"Graf 1"]

Plot[2*(x^2)+3*x+2,{x,-5,5}]

Manipulate[Plot[a*(x^2)+b*x+c,{x,-5,5},PlotRange->{Automatic,{-50,50}}],{a,-2,2},{b,-10,10},{c,-5,5}]

ClearAll[y]
res2=DSolve[{y''[t]+2*y'[t]+3*y[t]==Sin[2*t],y[0]==1,y'[0]==0},y[t],{t}][[1]];
y=y[t]/.res2

Plot[y,{t,0,20},PlotStyle->{Red,Thick,Dashed},AxesLabel->{"y","f (y)"}]
ClearAll[y]

ClearAll[y]
resDif=DSolve[{y''[t]+2*y'[t]+3*y[t]==Sin[2*t],y[0]==1,y'[0]==0},y[t],t];

proPlot=y[t]/.resDif[[1]];
Plot[proPlot,{t,0,20},PlotStyle->{Red,Thick,Dashed},AxesLabel->{"y","f (y)"}]

ClearAll[funkce]
funkce[x_]:=((Sin[x]*(E^x)+(x^2)-Cos[x])/((x^2)+1))

funkce[a]

b=Cos[x];

funkce[b]

funkce[x_,y_]:=x*y
funkce[{x_,y_}]:=(x/y)

funkce[a,c]
funkce[{a,c}]
funkce[a]

(*Zde zacina trei cviceni 7.3.2016 *)

res=Solve[7*(x^3)+m*(x^2)+9*x==17,x];
x1=x/.res[[1]];
x2=x/.res[[2]];
x3=x/.res[[3]];

proPlot=Abs[x1+x2-x3];
Plot[proPlot,{m,1,100},PlotLabel->Text[Style["Divnej Plot :-)",Pink,Italic,24]],AxesLabel->{Text[Style["m",Blue,"Times",20]],Text[Style["x1+x2-x3",Blue,"Times",20]]},PlotStyle->{Thick,Red}]

Plot[proPlot,{m,1,100},PlotLabel->"Plot",AxesLabel->{"m","x"},PlotStyle->{Thick,Red}]

Times

SeedRandom[1]
data=Table[{x,(x^2)+10Random[]},{x,1,10,0.1}];

plotList=ListPlot[data,AxesLabel->{"U","R"},PlotStyle->{Red,PointSize[0.01]}];

line = Fit[data, {1,x,(x^2),Log[x]},x]
fitPlot=Plot[line,{x,0,10}];

Show[plotList,fitPlot]

FindRoot[Cos[x]==x,{x,Pi}]

Solve[Cos[x]==x,x]

FindRoot[Sin[x]==0,{x,(π/2)}]

Solve[(x^3)==27.,x]
FindRoot[(x^3)==27.,{x,-1.5+2I}]

FindRoot[{(x^2)+y==2,x-y==3},{x,1},{y,2}]

NDSolve[{y'[x]==y[x]Cos[x+y[x]],y[0]==1},y[x],{x,0,30}]

DSolve[{y'[x]==a*Cos[x],y[0]==1},y[x],x]

res2=NDSolve[{y'[x]==y[x]Cos[x+y[x]],y[0]==1},y[x],{x,0,100}]

yres=y[x]/.res2[[1]];

Plot[yres,{x,0,100},PlotStyle->Thick]

res3=NDSolve[{Cos[y'''[t]]+y''[t]-2==(E^(-t))*Sin[t],y[0]==1,y'[0]==2,y''[0]==3},y[t],{t,0,15},MaxSteps->100000]

yT=y[t]/.res3[[1]];

Plot[yT,{t,0,15},PlotStyle->{Green,Dashed,Thick},AxesLabel->{" osa X "," osa Y "}]

(*Zde zacina cv.4*)

ClearAll[f]
f[a_]:=x/.FindRoot[Sin[x]==0,{x,a}];
data=Table[{(a^2),f[a]},{a,0,20,0.5}];
ListPlot[data,PlotStyle->{Red,PointSize[0.05]},AxesLabel->{"(a^2)","f(a)"}]

R1=100;
R2=1000;
R3=200;
L1=0.1;
L2=0.002;
kap=50*(10^(-6));
Uz=50Tanh[100Sin[314*t]];
Iz=Sin[314*t+0.1];
rceUzly={Iu[t]==Ic[t]+IR1[t],IR1[t]+IL1[t]==IR2[t],Ic[t]+Iz==IL1[t],IR2[t]+IL2[t]==0};

rceSoucastky={Ic[t]==kap*D[Uc[t],t],Uc[t]==U1[t]-U3[t],U1[t]-U2[t]==R1*IR1[t],U3[t]-U2[t]==L1*D[IL1[t],t],U2[t]-U4[t]==R2*IR2[t],0-U4[t]==L2*D[IL2[t],t],0-U1[t]==Uz};

pocPodm={Uc[0]==0,IL1[0]==0,IL2[0]==0};

rce=Union[rceUzly,rceSoucastky,pocPodm];

nezname=Union[Cases[rce,_Symbol[t],{0,∞}]]

res=NDSolve[rce,nezname,{t,0,0.6},StartingStepSize->(10^(-12)),MaxSteps->100000];

proPlot={Uz,U3[t]}/.res
Plot[proPlot,{t,0,0.06}]

Union[Cases[rce,_Symbol[t],{0,Infinity}]];

rce//TreeForm;

Plot[1Sin[314*t+0.1],{t,0,0.04}]

Integrate[Tanh[100Sin[314*t]],t]