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Jun 19th, 2018
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  1. Clear[r];
  2.  
  3. Clear[z0];
  4.  
  5. contour = z0 + r Exp[I theta];
  6.  
  7. f = (z - 3)^2*(z^3 + 1);
  8.  
  9. integrand = ((D[f, z] / f ) /. z -> contour)*D[contour, theta];
  10.  
  11. indefintegral = Integrate[integrand, theta];
  12.  
  13. defintegral = (indefintegral /. {r->5, z0 -> 0, theta -> 2*Pi})-
  14. (indefintegral /. {r -> 5, z0-> 0, theta -> 0})
  15.  
  16. r = 5;
  17.  
  18. z0 = 3;
  19.  
  20. contour = z0 + r*Exp[I theta];
  21.  
  22. f = (z - 3)^2*(z^3 + 1);
  23.  
  24. integrand = ((D[f, z] / f ) /. z -> contour)*D[contour, theta];
  25.  
  26. defintegral = Integrate[integrand, {theta, 0, 2*Pi}]
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