Quiet@Remove["Global`*"];
$HistoryLength=2;
SetDirectory[NotebookDirectory[]]

Quiet@Remove["Global`*"];
FileNames["*.xls"];
dataReal=Import["koeficientyReal.xls"][[1]];
info=dataReal[[1]];
data1=Drop[dataReal,1];
A=Transpose[Drop[pom=Transpose[data1],-1]];
b=pom[[-1]];
LinearSolve[A,b]

nezname=(Subscript[x, #])&/@Range[Length[b]];
rovnice=Thread[A.nezname==b];
Solve[rovnice]

Quiet@Remove["Global`*"];
FileNames["*.xls"];
dataReal=Import["koeficientyReal.xls"][[1]];
maticeA=dataReal[[2;;,;;-2]];
b=dataReal[[2;;,-1]];
LinearSolve[maticeA,b];

Quiet@Remove["Global`*"];
FileNames["*.xls"];
dataReal=Import["koeficientyReal.xls"][[1]];
data1=Drop[dataReal,1];
A=Drop[#,-1]&/@data1;
b=Flatten@(Take[#,-1]&/@data1);
LinearSolve[A,b]

Quiet@Remove["Global`*"];
FileNames["*.xls"];
dataComplex=Import["koeficientyKomplex.xls"][[1]];
data1=Drop[dataComplex,{1,2}];
data2=(Partition[#,2]&/@data1)/.{re_Real,im_}:>re+I*im;
data1=data2;
A=Transpose[Drop[pom=Transpose[data1],-1]];
b=pom[[-1]];
reseni1=LinearSolve[A,b];
reseni1>>"res1";

Range[20]
Partition[%,2]

Quiet@Remove["Global`*"];
FileNames["*.xls"];
dataReal=Import["koeficientyKomplex.xls"][[1]];

maticeAre=dataReal[[3;;,1;;-4;;2]];
maticeAim=dataReal[[3;;,2;;-3;;2]];
maticeA=maticeAre+I*maticeAim;

Bre=dataReal[[3;;,-2]];
Bim=dataReal[[3;;,-1]];
B=Bre+I*Bim;
reseni2=LinearSolve[maticeA,B];
reseni1=<<"res1";
reseni1==reseni2
Union[reseni1-reseni2//Chop]

Quiet@Remove["Global`*"];
rce={{5,11,2}.{y''[t],y'[t],y[t]}==((Sin[t])/(t+1))};
pocs={y[0]==1,y'[0]==5};
tmax=50;
sol=NDSolve[Union[rce,pocs],y,{t,0,tmax}][[1]];
Plot[y[t]/.sol,{t,0,tmax},PlotRange->All];

Quiet@Remove["Global`*"];
rce={{5,11,2}.{y''[t],y'[t],y[t]}==((Sin[t])/(t+1))};
pocs={y[0]==1,y[1]==5};
tmax=50;
sol=NDSolve[Union[rce,pocs],y,{t,0,tmax}][[1]];
Plot[y[t]/.sol,{t,0,tmax},PlotRange->All];

Quiet@Remove["Global`*"];
pom=MatrixPower[(({{1, 2}, {7, 13}})),(1/5)]//N
pom.pom.pom.pom.pom//Chop

(x^3)//TreeForm

Attributes[Sin]
Sin[{1,2,3}]

Attributes[Power]

Quiet@Remove["Global`*"];

(((({{1, 2}, {7, 13}})))^(1/5))

Quiet@Remove["Global`*"];
$HistoryLength=2;
SetDirectory[NotebookDirectory[]];
λ[T_]:=0.4+0.1T;
rce=D[λ[T[x]]*T'[x],x]==0;
d=0.5;
sol[der0_?NumericQ]:=T[d]/.NDSolve[{rce,T[0]==20,T'[0]==der0},T,{x,0,d}][[1]];
solder=FindRoot[sol[der]==100,{der,200}];
vys=NDSolve[{rce,T[0]==20,T'[0]==der/.solder},T,{x,0,d}][[1]];
Plot[T[x]/.vys,{x,0,d},PlotStyle->{Red,Thickness[0.006]},AxesLabel->{"x[m]","T[°C]"},GridLines->Full]

Quiet@Remove["Global`*"];
$HistoryLength=2;
SetDirectory[NotebookDirectory[]];
λ[T_]:=0.4+0.1T;
rce=D[λ[T[x]]*T'[x],x]==0;
d=0.5;
sol[der0_?NumericQ]:=T[d]/.NDSolve[{rce,T[0]==20,T'[0]==der0},T,{x,0,d}][[1]];
solder=FindRoot[sol[der]==100,{der,200}];
vys=NDSolve[{rce,T[0]==20,T'[0]==der/.solder},T,{x,0,d}][[1]];
Plot[T[x]/.vys,{x,0,d},PlotStyle->{Red,Thickness[0.006]},AxesLabel->{"x[m]","T[°C]"},GridLines->Full];

Quiet@Remove["Global`*"];
f[x_]:=Sin[Pi*x]+Cos[E*x];
Δx=0.1;
der1[x_]:=((f[x+Δx]-f[x])/(Δx));
der2[x_]:=((f[x+Δx]-f[x-Δx])/(2*Δx));
Plot[{der1[x]-f'[x],der2[x]-f'[x]},{x,0,3},PlotStyle->{Red,Blue}];
a=((der1[x+Δx]-der1[x])/(Δx));
b=((der2[x+Δx]-der2[x-Δx])/(2*Δx));
c=((der2[x+Δx]-der2[x])/(Δx));
d=((der1[x+Δx]-der1[x-Δx])/(2*Δx));
e=((f[x+Δx]+f[x-Δx]-2*f[x])/((Δx)^2));
k=60;
Plot[#-f''[x],{x,0,3},PlotRange->{Automatic,{-k*Δx,k*Δx}}]&/@{a,b,c,d,e}

Quiet@Remove["Global`*"];
f0=50.123;
ω=2*Pi*f0;
T=(1/f0);
f[t_]:=10*Sin[ω*t+0.456]+3.2;
data=Table[{t,f[t]},{t,0,5T,0.01T}];
ListPlot[data];
pom1=Partition[data,3,1];
test[{{t1_,u1_},{t2_,u2_},{t3_,u3_}}]:=u1<u2>u3;
pom2=Select[pom1,test]
fity=Fit[#,{1,x,(x^2)},x]&/@pom2;
maxima=x/.Solve[D[#,x]==0,x][[1]]&/@fity
{-1,1}.#&/@Partition[maxima,2,1]
((Mean[%]-T)/T)*1000

Quiet@Remove["Global`*"];
f0=50.123;
ω=2*Pi*f0;
T=(1/f0);
f[t_]:=10*Sin[ω*t+0.456]+3.2+0.01*RandomReal[{-1,1}];
data=Table[{t,f[t]},{t,0,5T,0.01T}];
ListPlot[data];
pom1=Partition[data,3,1];
test[{{t1_,u1_},{t2_,u2_},{t3_,u3_}}]:=u1<u2>u3;
pom2=Select[pom1,test]
fity=Fit[#,{1,x,(x^2)},x]&/@pom2;
maxima=x/.Solve[D[#,x]==0,x][[1]]&/@fity
{-1,1}.#&/@Partition[maxima,2,1]
((Mean[%]-T)/T)*1000