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This book is an introduction to basic Complex Analysis at the undergraduate and postgraduate levels.
Key Features * An integrated approach to the concept of differentiation for complex valued functions of a complex variable * Unified Cauchy Riemann equations * A detailed discussion on the construction of Riemann surfaces for elementary functions leading to its abstract concept * Step-by-step development of the most general form of Cauchy's theorem * Complex version of the real intermediate value theorem * Exhaustive treatment of contour integration and an introduction to the theory of univalent functions on the unit disc including a brief history of the Bieberbach's conjecture and its solution
New to the Second Edition: * Complete section on Analytic automorphisms on plane domains
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