1+1

(Sqrt[5])

(Sqrt[4])

(Sqrt[5.])

N[(Sqrt[5])]

N[(Sqrt[5]),25]

N[2,2]

(5^2)

LaplaceTransform
function=25

function*2

Solve[(x^2)+2*x+5*t==1,x]

t=5

list={1,5,{3,2},4,6}

list[[3,2]]

FullForm[list]

N[Sin[Cos[(E^Pi)]]]

t

t=25

ClearAll[t]

mySolve=Solve[(x^2)+2*x+5*t==1,x]

mySolve[[1]]

Plot[(E^x)*(E^(Sin[(x^2)])),{x,0,6Pi}]

mySolve=Solve[(x^2)+2*x+5*t==1,x]

x=x/.mySolve[[1]]

Plot[-1-(Sqrt[2-5 t]),{t,-5,5}]

ClearAll[x]
myRules={x->10,x->2,x->3}

x/.myRules

myRules2={x->1,y->2,z->3}

{x+y,y,y+a}/.myRules2

mySolve=Solve[5*x==1,x]

Plot[x/.mySolve,{x,1,5}]

myList={1,5,4,6,8,9}

myList[[-1]]

Length[myList]

Sort[myList]

N[(Sqrt[5])]

(Sqrt[5])//N

N@(Sqrt[5])

(*Second lecture*)

sol={x,y}/.Solve[{x+y-t==2,x+t-y==5},{x,y}][[1]]

t=2;
Plot[sol,{t,2,5},PlotLabel->"My Plot",AxesLabel->{"t","f1(t),f2(t)"},PlotStyle->{{RGBColor[0,0,1], Thick,Dashing[0.02]},{Thickness[0.01],Red}}]

??Plot

pl1=Plot[{Sin[(E^x)]*(E^x),Cos[(E^x)]*E},{x,1,10},PlotStyle->{{Blue,Thick,Dashed},{Red,Thickness[0.001]}},AxesLabel->{"x","sin[(E^x)]*(E^x),cos[(E^x)]*E"}]

SetDirectory[NotebookDirectory[]]

Export["graph.jpg",pl1,ImageResolution->400];

ClearAll[t]
Manipulate[Plot[Sin[k*t],{t,0,2*Pi},PlotStyle->Thick,PlotRange->{Automatic,{-2,2}}],{k,1,50}];

Print["It is OK!"];

sol=Solve[(x^2)+a*x+5==0,x];
x1=x/.sol[[1]];
x2=x/.sol[[2]];
Print["x1 = ",x1," x2 = ",x2 ];

DSolve

Series[Sin[x],{x,0,15}]

n=5;
(∑_(i=0)^n)(Subscript[a, i])*(x^i)==0
Solve[%,x]

DSolve

DSolve[y'[x]+(x^2)*((y[x])^2)==x Sin[x],y[x],x]

dsol=y[x]/.NDSolve[{y'[x]==y[x]*Cos[x+y[x]],y[-5]==1},y[x],{x,-5,30}][[1]]

Plot[dsol,{x,-5,30},PlotRange->All]

??NDSolve

R1=100;
R2=1000;
L1=0.01;
L2=0.5;
L3=0.02;
C1=0.005;
R3=100;
C3=0.003;
U=100*Sin[314*t+3];
IZ1=10*Sin[314*t];
IZ2=5*Sin[314*t];

equVolt={U5[t]-U1[t]==R2*IR2[t],IC3[t]==C3*U1'[t],U1[t]-U6[t]==L3*IL3'[t],U1[t]-U3[t]==L2*IL2'[t],U1[t]-U2[t]==R1*IR1[t],IC1[t]==C1*UC1'[t],UC1[t]==U6[t]-U3[t],U2[t]==-U,U2[t]-U3[t]==L1*IL1'[t],U3[t]-U4[t]==R3*IC2[t]};

Nodes={IR2[t]==IC3[t]+IR1[t]+IL2[t]+IL3[t],IR1[t]==IU[t]+IL1[t],IL1[t]+IL3[t]+IC1[t]==IC2[t],IZ2+IC2[t]==0,IZ1==IR2[t],IL3[t]==IC1[t]};

InCon={U1[0]==0,IL3[0]==0,IL2[0]==0,UC1[0]==0,IL1[0]==0};
var={U1,U2,U3,U4,U5,U6,IR1,IR2,IU,IL1,IL2,IL3,IC1,IC2,IC3};

AllEqu=Union[equVolt,Nodes,InCon];

_________________________________

R1=100;
R2=1000;
R3=100;
L1=0.01;
L2=0.5;
Con=0.003;
U=230*Tanh[100*Sin[314*t]];
IZ1=10*Sin[314*t];

equ2={U2[t]-U1[t]==R3*IR3[t],U1[t]-U4[t]==L1*IL1'[t],IC[t]==Con*U4'[t],U1[t]==R1*IR1[t],U1[t]-U3[t]==L2*IL2'[t],U1[t]-U3[t]==R2*IR2[t],U3[t]==-U};

Nodes2={IR3[t]==IL1[t]+IL2[t]+IR1[t]+IR2[t],IZ1==IR3[t],IL2[t]+IR2[t]==IU[t],IL1[t]==IC[t]};

InCon2={IL1[0]==0,U4[0]==0,IL2[0]==0};

var2={U1,U2,U3,U4,IR1,IR2,IR3,IU,IL1,IL2,IC};

AllEqu2=Union[equ2,Nodes2,InCon2];

sol=IC[t]/.NDSolve[AllEqu2,var2,{t,0,0.05},StartingStepSize->(10^(-15)),MaxSteps->100000][[1]]

Plot[{U,sol},{t,0,0.05}]

Manipulate[Plot[230*Tanh[k*Sin[314*t]],{t,0,0.05}],{k,1,100}]

SetDirectory[NotebookDirectory[]]

data=Import["scope_7.csv"];

data2=Cases[data,{_Real,_Real,_Real,_Real}]

dataForCurrentRaw=data2/.{t_,U1_,i_,U2_}:>{t,i};

{{-0.0199`,0.445939705`,-0.068121858`,-0.369849242`},{-0.019895`,0.473678398`,-0.068121858`,-0.411457282`},{-0.01989`,0.445939705`,-0.066363064`,-0.369849242`},{-0.019885`,0.45056282`,-0.066111808`,-0.369849242`}}/.{t_,U1_Real,i_,U2_}:>{t,i}

(5+I)[[0]]

dataForCurrent=MovingAverage[dataForCurrentRaw,100];
ListPlot[dataForCurrent]
intDataCurrent=Interpolation[dataForCurrent]
tmin=0;
tmax=intDataCurrent[[1,1,2]];

R1=100;
R2=1000;
R3=100;
L1=0.01;
L2=0.5;
Con=0.003;
U=230*Tanh[100*Sin[314*t]];
IZ1=100*intDataCurrent[t];

equ2={U2[t]-U1[t]==R3*IR3[t],U1[t]-U4[t]==L1*IL1'[t],IC[t]==Con*U4'[t],U1[t]==R1*IR1[t],U1[t]-U3[t]==L2*IL2'[t],U1[t]-U3[t]==R2*IR2[t],U3[t]==-U};

Nodes2={IR3[t]==IL1[t]+IL2[t]+IR1[t]+IR2[t],IZ1==IR3[t],IL2[t]+IR2[t]==IU[t],IL1[t]==IC[t]};

InCon2={IL1[0]==0,U4[0]==0,IL2[0]==0};

var2={U1,U2,U3,U4,IR1,IR2,IR3,IU,IL1,IL2,IC};

AllEqu2=Union[equ2,Nodes2,InCon2];

sol=IC[t]/.NDSolve[AllEqu2,var2,{t,tmin,tmax},StartingStepSize->(10^(-15)),MaxSteps->200000][[1]]

Plot[{sol,IZ1},{t,0,0.0255}]

f=50;
equation={Uz-U1[t]==R*IR[t],IC[t]==cond*U1'[t],IR[t]==IC[t],U1[0]==5}/.{R->100,cond->10*(10^(-6)),Uz->10*Sin[2*Pi*f*t+0.34]}

u1=U1[t]/.NDSolve[equation,Union[Cases[equation,_Symbol[t],Infinity]],{t,0,0.1}][[1]]

Plot[u1,{t,0,0.1}]

InputForm[u1];
Plot[{1.5Sin[3*x+0.4]+0.5Sin[3*x+0.7],0.5Sin[3*x+0.7],1.5Sin[3*x+0.4]},{x,0,2*Pi}]

ParametricPlot[{Re[(E^(I*psi))],Im[(E^(I*psi))]},{psi,0,2Pi}]