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Ideal for an introductory course in complex analysis at the advanced undergraduate or graduate level, this text has been developed over decades of teaching with an enthusiastic student reception. The first half of the book focuses in the core material. An early chapter on power series gives the reader concrete examples of analytic functions and a review of calculus. Mödius transformations are presented with emphasis on the geometric aspect and the Cauchy theorem is covered in the classical manner. The remaining chapters provide an elegant and solid overview of special topics such as Entire and Meromorphic Function, Analytic Continuation, Normal families, Conformal Mapping, and Harmonic Functions.
Key Features:
• Power Series approach gives students a chance to review calculus and discover complex analysis is a natural extension of calculus
• Unique coverage of Phragmén-Lindelöf Theorem (§10.4), the Runge Approximation Theorem (§6.6), Conformal Mappings of Multiply-Connected Regions (§7.9), and Extensions of Theorems of MittagLeffler and Weierstrass (§7.3)
• Also unique is the comparisons of Complex Analysis and Real analysis in Chapter 4,5, and 9
• New, elementary proof of the Picard Theorems in Chapter 12
• Generous exercise sets are a treasure trove of interesting and challenging problems
• Over 60 illustrations help the reader visualize complex relationships
ISBN - 9789380108957
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Pages : 430
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