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.*