Re: "Complex" Integral

• To: mathgroup at smc.vnet.net
• Subject: [mg125900] Re: "Complex" Integral
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Fri, 6 Apr 2012 05:57:23 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201204050958.FAA13384@smc.vnet.net>

```q1 = Cos[\[Theta]] + 1;
q2 = Cos[\[Theta]] - 1;
q3 = 2*Sin[\[Theta]];
q4 = 2*Cos[\[Theta]];
a = Sqrt[Cos[\[Theta]]]; (* cannot use a=sqrt(Cos[\[Theta]]) *)

e = (a/2)*(q1 + q2*Cos[2*\[Phi]]);
(* your notebook erroneously contains TextCell[""] embedded in \
equation for e *)

f = e*(E^(I*k*\[Rho]*Sin[\[Theta]]*Cos[\[Phi] - ph])*
E^(I*k*z*Cos[\[Theta]])*
Sin[\[Theta]]);

\[Lambda] = 600/10^9;
n = 1;
k = 2*(Pi/\[Lambda]);
z = 0;
\[Rho] = 100/10^9;
ph = 1;

g = Re[f] // ComplexExpand // FullSimplify;

Plot3D[g, {\[Theta], 0, 2*Pi}, {\[Phi], 0, 1.2}]

NIntegrate[g, {\[Theta], 0, 2*Pi}, {\[Phi], 0, 1.2}] // Chop

-0.0669811

f = f // ComplexExpand // FullSimplify;

NIntegrate[f, {\[Theta], 0, 2*Pi}, {\[Phi], 0, 1.2}]

-0.0669811 + 0.675092 I

Bob Hanlon

On Thu, Apr 5, 2012 at 5:58 AM, Elad <eladarbel at hotmail.com> wrote:
> Hi Guys,
>
> Im trying to calculate a the integral over the function f(Theta,Phi ; Rho,ph,z ; k)
> [Theta -> 0..2 Pi, Phi ->0..1.2],  for a given values of  [Rho,ph,z ; k]
>
> actually i need to calculate f[] for a broad range of values for [Rho,ph,z].
>
>
> f = (1/2)*
>  E^(I*k*z*Cos[\[Theta]] + I*k*\[Rho]*Cos[ph - \[Phi]]*Sin[\[Theta]])*
>  sqrt*Cos[\[Theta]]*
>    (1 + Cos[\[Theta]] + (-1 + Cos[\[Theta]])*Cos[2*\[Phi]])*
>  Sin[\[Theta]]
>
> Im new with Mathematica, and ive read the documentation but probably im doing something wrong,
> Ive also tried to plot the surface for given values of  [Rho,ph,z ; k] without much success.
>
> Here is a link to notebook where i tried to plot the surface (from my dropbox):
> http://dl.dropbox.com/u/50792162/B1.nb
>
> I would appreciate it if you guys could help me out with it.
>
> 10x