A Course in Complex Analysis

1. Front Matter

   Pages i-viii

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2. Analysis in the complex plane

   • Wolfgang Fischer, Ingo Lieb

   Pages 1-35

3. The fundamental theorems of complex analysis

   • Wolfgang Fischer, Ingo Lieb

   Pages 36-70

4. Functions on the plane and on the sphere

   • Wolfgang Fischer, Ingo Lieb

   Pages 71-107

5. Integral formulas, residues, and applications

   • Wolfgang Fischer, Ingo Lieb

   Pages 108-147

6. Non-elementary functions

   • Wolfgang Fischer, Ingo Lieb

   Pages 148-192

7. Meromorphic functions of several variables

   • Wolfgang Fischer, Ingo Lieb

   Pages 193-213

8. Holomorphic maps: Geometric aspects

   • Wolfgang Fischer, Ingo Lieb

   Pages 214-257

9. Back Matter

   Pages 258-272

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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.

• Complex Analysis
• Functions of complex numbers
• Funktionentheorie
• Holomorphic Functions
• Komplexe Analysis

• Faculty 3 - Mathematics, University of Bremen, Bremen, Germany

  Wolfgang Fischer

• Mathematical Institute, University of Bonn, Bonn, Germany

  Ingo Lieb

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

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