5*2

2*(Sqrt[2])

(3^(2^(2^2)))

(1/((((2/3)/3)/2)/4))

(25/4)

((a+b)/c)

2*(Sqrt[2])

2*(Sqrt[2.])

N[2*(Sqrt[2]),100]

N[1/18];
Sin[2.];

(*komentar*)

sin=10;
x*(sin(2)+2)

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

N[E];

Solve[Sin[t]==1,t];
FindRoot[Sin[t]==0,{t,(Pi/2)}]

ClearAll[y,a,b,c]

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

N[(Sqrt[2]),10]
(Sqrt[2])//N
N@(Sqrt[2])

x=5;
x+Sin[10]//N

a=3;
b=5;
%

%

Limit[Log[x*y-1],{x->0,y->0}]

kk=LaplaceTransform[(t^4)Sin[t],t,p]

InverseLaplaceTransform[kk,p,t]

Integrate[(t^17)*Cos[t],{t,10,20.}]

(∫_10^20.)(t^17)*Cos[t]\[DifferentialD]t

(5/3)+1.

(*2. cviceni 23.2.2015*)

DSolve[{x''''[t]+14*x''[t]+40*x[t]==Cos[t],x'''[0]==1,x''[0]==0,x'[0]==2,x[0]==2},x[t],t]

Plot[Sin[t],{t,0,6Pi}]

?/.

{a,aa,aaa,aaaa}/.aa->10

aa

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

ClearAll[a,b]

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

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

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

{{a,aa},{aaa,aaaa}}[[-1]]

{{a,aa},{aaa,aaaa}}[[2]]

{{a,aa},{aaa,aaaa}}//TreeForm

res1=x[t]/.DSolve[{x''''[t]+14*x''[t]+40*x[t]==Cos[t],x'''[0]==1,x''[0]==0,x'[0]==2,x[0]==2},x[t],t][[1,1]];

t=debil;

Plot[{res1,3*Sin[t]},{t,0,10},AxesLabel->{"t[s]","I[A]"},PlotLabel->"Nazev grafu",PlotLegends->{"res1","3*Sin[t]"},PlotStyle->{{Magenta,Thick},{DotDashed,Thickness[0.01],Orange}},PlotRange->{Automatic,{0,3}}]

?*Plot*;

Blue

res2={x,y}/.Solve[{a*(x^2)+y-5==0,y+x==3},{x,y}][[2]]

Plot[res2,{a,1,15},PlotStyle->{{Thick,Red},{Thick,Dashed,Brown}},AxesLabel->{"a","x[a],y[a]"},PlotLabel->"Graf"]

Solve[{a*(x^2)+y-5==0,y+x==3},{x,y}]

(*Zdše zacina treti cviceni 2.3.2015*)

res=FindRoot[{Tan[x]==2*Sin[y],Cot[y]==2*Sin[x]},{{x,1.5},{y,0.5}}];
iks=x/.res;
yps=y/.res;
Plot[{iks*Sin[yps*t],yps*Sin[iks*t]},{t,0,30},PlotStyle->{{Blue,Thick},{Magenta, Thick}},AxesLabel->{"t[s]","sin1 ,sin2"},PlotLabel->"sin1, sin2"]

res=FindRoot[{Tan[x]==2*Sin[y],Cot[y]==2*Cos[x]},{{x,1.5},{y,0.5}}];
iks=x/.res[[1]];
yps=y/.res[[2]];

Manipulate[Plot[{iks*Sin[yps*t+φ1],yps*Sin[iks*t-φ2]},{t,0,30},PlotStyle->{{Magenta,Thick},{Blue,Thick}},AxesLabel->{"t [s]"," sin1, sin2"},PlotLabel->"sin1,sin2"],{φ1,0,2π},{φ2,0,2*Pi}]

(*Plot[{x*Sin[y*t],y*Sin[x*t]}/.res,{t,0,30}]*)

Manipulate[Plot[{iks*Sin[yps*t+φ1],yps*Sin[iks*t-φ2]},{t,0,30},PlotStyle->{{Magenta,Thick},{Blue,Thick}},AxesLabel->{"t [s]"," sin1, sin2"},PlotLabel->"sin1(φ1="<>ToString[Round[φ1,0.01]]<>")"],{φ1,0,2π},{φ2,0,2*Pi}]

ClearAll[mojeFunkce]
mojeFunkce[a_,b_,c_]:=Solve[a*(x^2)+b*x+c==0,x]

mojeFunkce[1,2,3]

ClearAll[mojeFunkce]
mojeFunkce[a_,b_,c_]:=Module[{res,x1,x2,x},

res=Solve[a*(x^2)+b*x+c==0,x];
x1=x/.res[[1]];
x2=x/.res[[2]];
N[{x1,x2}]
]

mojeFunkce[a,b,c]

Sum[mojeFunkce[i,2*i,3*i][[1]],{i,1,10}]

Plus@@Table[mojeFunkce[i,2*i,3*i][[1]],{i,10}]

prom=Plus@@Table[mojeFunkce[i,2*i,3*i],{i,10}]
prom[[1]]

Plus@@Table[mojeFunkce[i,2*i,3*i][[1]],{i,10}]

prom1=Plus@@Table[mojeFunkce[i,2*i,3*i],{i,10000}]
prom1[[1]]
Times[prom1[[1]]]

Times[Plus@@Table[mojeFunkce[i,2*i,3*i][[1]],{i,10}]]

(* ctvrte cviceni 9.3.2015*)

NDSolve

R1=100;
R2=1000;
R3=500;
R4=15;
C1=10*(10^(-9));
C2=4.7*(10^(-6));
L=0.15;
UZ=10Sin[2*Pi*50*t];
IZ=Tanh[(((Sin[2*Pi*50*t]))^50)];

rceUzly={Iuz[t]==IR1[t],IR1[t]==IL[t]+IC1[t],IL[t]+IR2[t]==0,IC1[t]==IR3[t],IR3[t]==IR2[t]+IC2[t],IC2[t]+IR4[t]==0,IZ+IR4[t]==0};

rceSoustatky={U1[t]-U2[t]==R1*IR1[t],UZ==-U1[t],U2[t]-U3[t]==L*IL'[t],IL[0]==0,IC1[t]==C1*UC1'[t],UC1[t]==U2[t]-U4[t],UC1[0]==0,U5[t]-U3[t]==R2*IR2[t],U4[t]-U5[t]==R3*IR3[t],IC2[t]==C2*UC2'[t],UC2[t]==U5[t]-U6[t],UC2[0]==0,U7[t]-U6[t]==R4*IR4[t]};
rceVse=Union[rceUzly,rceSoustatky]

nezname=Union[Cases[rceVse,_Symbol[t],{0,Infinity}]]

rceVse//TreeForm;

res=NDSolve[rceVse,nezname,{t,0,1},StartingStepSize->(10^(-12)),MaxSteps->(10^5)]

uc2res=U2[t]/.res[[1]]
Plot[uc2res,{t,-0,0.5},PlotStyle->{Red,Blue}]

(*Zde zacina 5.cv 16.3.2015*)

rceUzly={Iuz==IR1,IR1==IR2+IR3,IR3==IR4+Iout,IR2+Iz==0};
rceSoucastky={U1-U2==R1*IR1,U2-U3==R3*IR3,U2-U4==R2*IR2,U3==R4*IR4,U1==Uz};

rceVse=Union[rceUzly,rceSoucastky];

res=Solve[rceVse,{U1,U2,U3,U4,Iuz,IR1,IR2,IR3,IR4}];

U3/.res[[1]]/.{R1->10.,R2->350,R3->1000,R4->500,Iz->15,Uz->15000.}//Expand

(a+b)*(a-b)//Expand

(I^I)//ComplexExpand

ClearAll[par,ser];
par[list_]:=(((Plus@@((list^(-1)))))^(-1));
ser[list_]:=Plus@@list;

k=1000.;
μ=(10^(-6));
m=0.001;
dos={R1->10k,c1->1μ,c2->2μ,R2->1,R3->1(k^2),R4->1,R5->1,L1->1m,L2->2m,L3->2m};
za=ser[{R2,I*ω*L1}];
zb=par[{za,R3}];
z1=ser[{zb,R1,(1/(I*ω*c1))}];
zc=ser[{(1/(I*ω*c2)),R4}];
zd=par[{zc,I*ω*L2}];
z2=ser[{zd,R5,I*ω*L3}];
zIn=ser[{z1,z2}];
ZinCiselne=zIn/.dos;
LogLogPlot[Abs[ZinCiselne],{ω,100,4*(10^6)},PlotRange->All,AxesLabel->{"ω [(s^(-1))]","Abs[Zin] [Ω]"},GridLines->Automatic,PlotStyle->{Red,Thickness[0.006]},PlotPoints->10000]

LogLinearPlot[Arg[(z2/(z1+z2))/.dos],{ω,0.01,4*(10^9)},PlotRange->All,AxesLabel->{"ω [(s^(-1))]","Arg[P] [1]"},GridLines->Automatic,PlotStyle->{Red,Thickness[0.006]},PlotPoints->10000]

d={L1->20,L2->5L1};
3L1+L2//.d

Z1n=ser[{I*ω*L2,par[{ser[{I*ω*L1,R1}],R3}]}];
Z2n=ser[{R1,I*ω*L3,par[{(1/(I*ω*c2)),R3}]}];
proGraf=(Z2n/(Z2n+Z1n))/.dos;

LogLogPlot[Abs[proGraf],{ω,0.0001,4*(10^12)},PlotRange->All,AxesLabel->{"ω [(s^(-1))]","Abs[P] [-]"},GridLines->Automatic,PlotStyle->{Orange,Thickness[0.006]},PlotPoints->10000]