A Course in Complex Analysis: From Basic Results to Advanced Topics

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Springer Science & Business Media, Oct 21, 2011 - Mathematics - 280 pages
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This carefully written textbook is an introduction to the beautiful concepts and results of complex analysis. It is intended for international bachelor and master programmes in Germany and throughout Europe; in the Anglo-American system of university education the content corresponds to a beginning graduate course. The book presents the fundamental results and methods of complex analysis and applies them to a study of elementary and non-elementary functions (elliptic functions, Gamma- and Zeta function including a proof of the prime number theorem …) and – a new feature in this context! – to exhibiting basic facts in the theory of several complex variables. Part of the book is a translation of the authors’ German text “Einführung in die komplexe Analysis”; some material was added from the by now almost “classical” text “Funktionentheorie” written by the authors, and a few paragraphs were newly written for special use in a master’s programme.
 

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Contents

Chapter I Analysis in the complex plane
1
Chapter II The fundamental theorems of complex analysis
36
Chapter III Functions on the plane and on the sphere
71
Chapter IV Integral formulas residues and applications
108
Chapter V Nonelementary functions
148
Chapter VI Meromorphic functions of several variables
193
Geometric aspects
214
Hints and solutions of selected exercises
258
Bibliography
263
Index of Symbols
265
Index
266
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About the author (2011)

Professor Dr. Wolfgang Fischer, University of Bremen, Faculty 3 - MathematicsProfessor Dr. Ingo Lieb, University of Bonn, Mathematical Institute

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