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MathGroup Archive 1999

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Mathematica help

  • To: mathgroup at smc.vnet.net
  • Subject: [mg20314] Mathematica help
  • From: Niguel Eames <Neames at ITA.CI.LA.CA.US>
  • Date: Fri, 15 Oct 1999 20:20:43 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Mathgroup,

I need help to resolve this integral and if it's possible show the solution
step by step.

I wonder if the integral could be plotted, in order to find a simpler function
that closely approximates the given function. The integral is a function of z`
and z (but a wanted to hold z constant at first).
 
E=[1+ (1/k^2)(2nd parital diff eq respect to z)]{2 Integral{sin[k(L-z`)] * Exp
{jkSqrt[(z-z`)^2 + a^2]} / Sqrt[(z-z`)^2 + a^2]}dz`}
 The limits are from 0 to L.

where,
                     z = L/2 (a try)
                     lamda = 3 meters
                     L = lamda/4 = 0.75 meters
                     a = 0.03 meters
                     k = 2 Pi/lamda
                     E = Electric field in the gap

I split the integral into the real and imaginary parts.  I attempted to
integral the imaginary part first.
I used Taylor series to approximate the function for L=0.4.  It turns out that
a fourth order expansion is a good approximation.  Mathematica was able to
integral it.  It seems unable to differentiate the integral and add to it the
original integral.  I would really appreciate your help with this difficult
problem. 
I have a copy of Mathematica for students version 3.0.0, license: L2709-1961,
running on a Pentium 333MHz with a Windows 98 OS.     

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                           


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