Series[Cos[x], {x, 0, 7}]

Series[Sin[x], {x, 0, 7}]

Series[Exp[I*x], {x, 0, 7}]

Plot[{Sin[x]^2, 0.5 - 0.5*Cos[2*x]}, {x, 0, 2  Pi}];

<< Calculus`VectorAnalysis`

SetCoordinates[Cartesian[x, y, z]];

hacko = {0, 0, Hz[y]};
Curl[hacko]

rov = Laplacian[hacko][[3]] == 
        I*γ*ω*μ*hacko[[3]]

res = DSolve[rov, Hz[y], y]

Simplify[
        Hz[y] /. res[[1]], {γ > 0, μ > 0, ω > 0}] // 
      N

((7. *(10^86)*7. *(10^86)*4*Pi*(10^(-7))*(10^(-6)))/(15*(10^9)*3600*24*365))

Plot[Exp[x], {x, 0, 200}, PlotRange -> All]

Hres = C2*Exp[-(1 + I)*(y/a)];

Curl[{0, 0, Hz[y]}]

ClearAll[Hz];
Hz[y_] = H0*Exp[-(1 + I)*(y/a)];
Jx[y_] = Curl[{0, 0, Hz[y]}][[1]]

proud = 
      Simplify[m*Integrate[Jx[y], {y, 0, ∞}], {a > 0}]

Ex[y_] = (1/γ) Jx[y]

napeti = Ex[0]*d

impedance = (napeti/proud)

jecko = {0, Jy[x], 0}

Laplacian[jecko] == ω*γ*μ*jecko

rce=Jy''[x]==I*γ μ ω Jy[x]

jz[x_] = Jy[x] /. DSolve[rce, Jy[x], x][[1]]

proud = m*Integrate[jz[x], {x, -(d/2), (d/2)}]

reskonst = Solve[{proud == I0, jz'[0] == 0}, {C[1], 
            C[2]}][[1]]

j[x_] = 
      FullSimplify[
        FullSimplify[
            jz[x] /. reskonst, {γ > 0, ω > 0, μ > 
                0}] /. (Sqrt[γ μ ω]) -> ((Sqrt[2])/a)]

try

cm = 0.01;
dtry = 20  cm;
try = 
        j[x] /. {I0 -> 1, d -> dtry, a -> 1  cm, 
            m -> 10  cm};
\(\(Plot[{Abs[try], 0}, {x, \(-dtry\)/2, dtry/2}, 
        PlotStyle -> {{Hue[0.63], Thickness[0.008]}, {GrayLevel[0], 
              Thickness[0.001]}}, 
        AxesLabel -> {"x", \*""Jy[A.\!\(m\^\(-2\)\)]""}, 
        PlotRange -> All];\)\)

(1/(((2  Pi)/ω))) 
      Integrate[
        Um*Sin[ω*t + fiu]*Imm*Sin[ω*t + fii], {t, 
          0, ((2  Pi)/ω)}]

<< Algebra`ReIm`

zrej[z_] := z /: Im[z] = 
          0;

    zrej /@ {fii, fiu, Um,  Imm, d, a, x, I0, 
          m, γ, ω};

Um*Exp[I*fiu]*Conjugate[Imm*Exp[I*fii]]

integrand = j[x]*Conjugate[j[x]]

integrand /. {x -> Random[], d -> Random[], a -> 1, 
        m -> 1, I0 -> 1}

ztraty = ((m*el)/γ) 
        Integrate[integrand, {x, -(d/2), (d/2)}]

ztraty /. d -> ξ*a

Plot[-((Sin[ξ] + Sinh[ξ])/(Cos[ξ] - 
              Cosh[ξ])), {ξ, 1, 4}]

Plot[-((Sin[ξ] + Sinh[ξ])/(Cos[ξ] - 
              Cosh[ξ])), {ξ, 0.1, 10}, 
      PlotRange -> All]

Simplify[
      D[((Sin[ξ] + Sinh[ξ])/(Cos[ξ] - Cosh[ξ])), ξ]]

((50.  + 273)/(10 + 273))

evect = {0, j[x]/γ, 0};
bevect = Curl[evect]/(-I*ω)

fvect = Cross[{0, j[x], 0}, Conjugate[bevect]]

sila = Re[fvect]