Use 'numframes', not 'frames'. See the help page for DEplot (not DEplot3d).

@hirnyk Yes, that was my point. It was intended as a counterexample to Axel Vogt's argument.

@hirnyk Yes, that was my point. It was intended as a counterexample to Axel Vogt's argument.

@Axel Vogt It was for you.

@Axel Vogt It was for you.

Take F(x) = x^2*sin(1/x) for x<>0 and F(0) = 0. Then F is  differentiable everywhere. The derivative at zero is zero by a direct application of the definition of differentiability.

However, F'(x) = 2*x*sin(1/x) -cos(1/x) doesn't have a limit at 0. 

Edited: This a counterexample to Axel Vogt's argument.

Take F(x) = x^2*sin(1/x) for x<>0 and F(0) = 0. Then F is  differentiable everywhere. The derivative at zero is zero by a direct application of the definition of differentiability.

However, F'(x) = 2*x*sin(1/x) -cos(1/x) doesn't have a limit at 0. 

Edited: This a counterexample to Axel Vogt's argument.

@Axel Vogt It seems that you are right. I'm glad that I said, "If Maple is right .. ".

eq:=(-t)^5=abs((t^2+t+1)/(-t));
eq2:=eval(eq,t=x+I*y) assuming x::real,y::real;
expand(%);
sys:={Re(lhs(%))=rhs(%),Im(lhs(%))=0} assuming real;
sol:=solve(sys,{x,y}):
evalf(sol):
L:=remove(has,[%],I);

Here Maple finds 3 solutions, but clearly if t is a solution then conjugate(t) is a solution, thus 5 solutions.

@Axel Vogt It seems that you are right. I'm glad that I said, "If Maple is right .. ".

eq:=(-t)^5=abs((t^2+t+1)/(-t));
eq2:=eval(eq,t=x+I*y) assuming x::real,y::real;
expand(%);
sys:={Re(lhs(%))=rhs(%),Im(lhs(%))=0} assuming real;
sol:=solve(sys,{x,y}):
evalf(sol):
L:=remove(has,[%],I);

Here Maple finds 3 solutions, but clearly if t is a solution then conjugate(t) is a solution, thus 5 solutions.

Since we are in the complex plane, abs(z) is not just either z or -z.

Since we are in the complex plane, abs(z) is not just either z or -z.

Not knowing the constants I just picked some, and did the following with no problem:

E_horiz := sqrt(E_theta^2 + E_phi^2):

param:={W=1, h=2, k0=3, kx=3, ky=4, l=5, epsr=6, seq(JX[i]=1/(1+i),i=1..80),epsre=7}:
res:=eval(E_horiz,param):
plot(res,theta=0..2*Pi);

Not knowing the constants I just picked some, and did the following with no problem:

E_horiz := sqrt(E_theta^2 + E_phi^2):

param:={W=1, h=2, k0=3, kx=3, ky=4, l=5, epsr=6, seq(JX[i]=1/(1+i),i=1..80),epsre=7}:
res:=eval(E_horiz,param):
plot(res,theta=0..2*Pi);

There is an obvious syntactical error in the statement E_horiz := subs(theta := Pi/2, E_horiz):

The assignment operator ':=' should be replaced by '=' of course.

What do you mean by

"I am looking for E_phi(theta), E_theta(theta), E_horiz(phi)."

?

When you say

'Maple cannot solve this line: "E_phi_magnitude := sqrt((Re(E_phi))^2 + (Im(E_phi))^2):".'

what do you mean by solve? There is no equation.

Since there are lots of names involved having no numeric values there is not much simplification that can be done.

There is an obvious syntactical error in the statement E_horiz := subs(theta := Pi/2, E_horiz):

The assignment operator ':=' should be replaced by '=' of course.

What do you mean by

"I am looking for E_phi(theta), E_theta(theta), E_horiz(phi)."

?

When you say

'Maple cannot solve this line: "E_phi_magnitude := sqrt((Re(E_phi))^2 + (Im(E_phi))^2):".'

what do you mean by solve? There is no equation.

Since there are lots of names involved having no numeric values there is not much simplification that can be done.