I have these three functions:

Phi := proc (z) options operator, arrow; z^(-(1/2)*alpha)*(BesselJ(alpha, 2*sqrt(lambda*alpha*z))-BesselY(alpha, 2*sqrt(lambda*alpha*z))*BesselJ(alpha, 2*sqrt(lambda*alpha*a))/BesselY(alpha, 2*sqrt(lambda*alpha*a))) end proc

w := proc (z) options operator, arrow; alpha*z^alpha end proc

Hello, again,
basically, I have an implicit relation for lambda:

> eq1 := (sqrt(lambda*alpha)+alpha)*BesselJ(alpha, 2*sqrt(lambda*alpha))/(2*sqrt(lambda*alpha)) = BesselJ(1+alpha, 2*sqrt(lambda*alpha))/alpha;

So solutions of lambda, for a particular alpha are given at the intersections of the two functions:

> plot({subs(alpha = 2, (sqrt(lambda*alpha)+alpha)*BesselJ(alpha, 2*sqrt(lambda*alpha))/(2*sqrt(lambda*alpha))), subs(alpha = 2, BesselJ(1+alpha, 2*sqrt(lambda*alpha))/alpha)}, lambda = 0 .. 50, -1 .. 1, color = [red, blue])

Hiya,

I have two questions...
Firstly when plotting a graph in Maple using plots[display]({A1,A2,A3}), is there anyway to switch the horizontal and vertical axes such that f(z) is on the horizontal axis and z along the vertical?

Secondly, I'm trying to plot a sum at various times t,

c(z,t):= Sum(A[n]*Phi[n](z)*exp(-lambda[n]*t), n = 1 .. 10)

Hiya,
I have an implicit equation;

> tan(beta)=-2/alpha*(beta);

where,

> beta:= sqrt(lambda*alpha-(alpha/2)^2);

for some dimensionless variable alpha.
I want to solve the equation for lamba and plot it as a function of beta.... but I don't know how to go about it.

Thanks for your help
k

Hiya, I'm trying to solve this pde in Maple:

> PDE:= diff(c(z,t),t) = k*diff(c(z,t),z$2) + w*diff(c(z,t),z); 

where k, w are constants, but I don't know how to apply the boundary conditions:

c(0,t)=0 and 0=k*diff(c(z,t),z$2) + w*diff(c(z,t),z) at z=h

and initial condition c=f(z) at t=0

I know by hand you would solve by separating variables, but is there an equivalent method in Maple?
Eventually I want to plot c(z) for given times to show how the solution evolves... but one thing at a time!