Mathematical methods Lecture 10 of 34

October 10, 2012 by Multimedia Publications and Printing Services

Lecturer: K.S. Narain , ICTP

lecture 10

  The Converse of the Cauchy theorem, Cauchy Criteria for Convergence,Geometric series


  •   If we know that there is a continuous function whose integral over any closed contour in some region vanishes then that function is analytic in that region.
  •  Then we showed that if f is continuous  for contour C(C is a closed
  • contour in some region R) then f(z) is analytic and in fact we proved it.
  • We prove Cauchy Criteria for Convergence and talk about uniform
  • Convergence and give some examples.
  • Necessary conditions for convergent series are provided 
  • We give some examples of convergency   like geometric series we also prove it.
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