Mathematical Methods Lecture 10 of 34

October 4, 2011 by K.S. Narain

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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