> restart;
> refresh(tools);
> with(plots);
> Digits := 5;
> h := 100;
> x := -h;
> u := 0.25;
> nu := (1-u)*(1/2);
> i := sqrt(-1);
> t := .1;
> D1 := 10^(-8);
> D2 := 10^(-6);
> k[1] := 1/sqrt(D1);
> k[2] := 1/sqrt(D2);
> with(Student[Calculus1]);
> M := proc (x, h) options operator, arrow; (k[1]*cosh(k[1]*rho^nu*exp(i*Pi*nu)*x)-k[2]*sinh(k[1]*rho^nu*exp(i*Pi*nu)*x))*exp(-rho*t)/((k[1]*cosh(k[1]*rho^nu*exp(i*Pi*nu)*h)+k[2]*sinh(k[1]*rho^nu*exp(i*Pi*nu)*h))*rho) end proc;
> a := ApproximateInt(M(x, h), rho = 0 .. 100);
> N := proc (x, h) options operator, arrow; (k[1]*cosh(k[1]*rho^nu*exp(-i*Pi*nu)*x)-k[2]*sinh(k[1]*rho^nu*exp(-i*Pi*nu)*x))*exp(-rho*t)/((k[1]*cosh(k[1]*rho^nu*exp(-i*Pi*nu)*h)+k[2]*sinh(k[1]*rho^nu*exp(-i*Pi*nu)*h))*rho) end proc;
> b := ApproximateInt(N(x, h), rho = 0 .. 100);
> p := evalf(1+a/(2*i*Pi)-b/(2*i*Pi));
> plot(p(-100, .1), -100 .. 0, 0 .. 1, colour = ["green"], axes = BOXED, labels = ["layer thickness, μm", "reduced concentration, C/C"], labeldirections = [horizontal, vertical]);