(*1.cviceni 22. 2. 2016*)
1+1

1+2

(* Takto se pise komentar. *)

(Sqrt[2])

(Sqrt[2.])

N[(Sqrt[2])]

Sin[1.5]

N[(Sqrt[2]),50]

LaplaceTransform
laplacetransform

a=5
b=3

a*b

c*d

c*a

Clear[a]

E=5

E

N[E]

21a

a21

a+6*f*(5+1a-(5-f))

{7,3,5}

Solve[2*x+y==4,3*x+y==5,x,y]

Solve[{2*x+y==4,3*x+y==5},{x,y}]

List[1,2.3,5]

TreeForm[{{5.5,5,8},3,{1,2,8.9,{4,5}}}]

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

(*zkratky: (Sqrt[\[Placeholder]]) ctrl+2, (x^\[Placeholder]) ctrl+6, (\[Placeholder]/\[Placeholder]) ctrl+/*)

(*recka pismena: κ Esc+pismeno+Esc)*)

N[π]

π//N

N@π

Plot[{Sin[x],Cos[x],Sin[x]*Cos[x]},{x,0,6Pi}]

(*zde zacina cviceni 2, 29.2.2016*)

Solve[{a*(x^2)+3*y+4==0,x+y-4==0},{x,y}]

Plot[((3-(Sqrt[9-64 a]))/(2 a)),{a,-10,5}](*chyba v syntaxi*)

res=Solve[{a*(x^2)+3*y+4==0,x+y-4==0},{x,y}]

{1,5,4,8,9}[[4]]
{1,5,4,{1,9,5,4},9}[[4,2]]

res[[2]]

x+y/.{x->3, y->5}

z+y/.{x->3, y->5}

x/.{x->3,x->4}

x/.{x->3,x->4}[[2]]

x1=x/.res[[1]];

x2=x/.res[[2]];
y1=y/.res[[1]];
y2=y/.res[[2]];

Plot[{x1,x2,y1,y2},{a,-5,10},AxesLabel->{"a","x1, x2, y1, y2"},PlotStyle->{{Red,Thick},{Green,Dashed},RGBColor[0.4,0.1,0.6],Hue[0.3]},PlotRange->{Automatic,{-10,15}}]

Plot[{x1,x2,y1,y2},{a,-5,10}]

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

Plot[2*(x^2)+3*x+1,{x,-5,5}]

Manipulate[Plot[a*(x^2)+b*x+c,{x,-5,5},PlotRange->{Automatic,{-10,10}}],{a,-1,1},{b,-2,2},{c,-5,5}]

res=y[t]/.DSolve[{y''[t]+2y'[t]+3y[t]==Sin[3t],y[0]==5,y'[0]==4},y[t],t][[1]];

Plot[res,{t,0,15},PlotStyle->{Red,Thick,Dashed},AxesLabel->{"t","y"}]

resDif=DSolve[{y''[t]+2*y'[t]+3*y[t]==Sin[3*t],y[0]==5,y'[0]==4},y[t],t];

proPlotDif=y[t]/.resDif[[1]];

Plot[proPlotDif,{t,0,15},PlotStyle->{Red,Thick,Dashed},AxesLabel->{"t","y"}]

Plot[Evaluate[y[t]/.DSolve[{y''[t]+2*y'[t]+3*y[t]==Sin[3*t],y[0]==5,y'[0]==4},y[t],t][[1]]],{t,0,15},PlotStyle->{Red,Thick,Dashed},AxesLabel->{"t","y"}]

ClearAll[funkce]
funkce[a_]:=(a^2)

funkce[5]

funkce[k]

funkce[a_,b_]:=a+b

funkce[5]

funkce[5,2]

funkce[{a_,b_}]:=a*b

funkce[5,2]

funkce[{5,2}]