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Mathematics  Complex Analysis
Title: Complex Analysis
Department: Mathematics
Author: Prof. P. A. S. Sree Krishna
University: IIT Guwahati
Type: WebLink
Abstract: Complex numbers, the topology of the complex plane, the extended complex plane and its representation using the sphere. Complex functions and their mapping properties, their limits, continuity and differentiability, analytic functions, analytic branches of a multiple-valued function. Complex integration, Cauchys theorems, Cauchys integral formulae. Power series, Taylor s series, zeroes of analytic functions, Rouches theorem, open mapping theorem. Mobius transformations and their properties. Isolated singularities and their classification, Laurents series, Cauchys residue theorem, the argument principle.
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