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A Course in Complex Analysis

From Basic Results to Advanced Topics

  • Textbook
  • © 2012

Overview

Authors:
  1. Wolfgang Fischer

    1. Faculty 3 - Mathematics, University of Bremen, Bremen, Germany

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    You can also search for this author in PubMed   Google Scholar

  2. Ingo Lieb

    1. Mathematical Institute, University of Bonn, Bonn, Germany

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    You can also search for this author in PubMed   Google Scholar

  • Complex Analysis for Bachelor and Master Studies

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Table of contents (7 chapters)

  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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Keywords

About this book

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.

Authors and Affiliations

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

    Wolfgang Fischer

  • Mathematical Institute, University of Bonn, Bonn, Germany

    Ingo Lieb

About the authors

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

Bibliographic Information

  • Book Title: A Course in Complex Analysis

  • Book Subtitle: From Basic Results to Advanced Topics

  • Authors: Wolfgang Fischer, Ingo Lieb

  • DOI: https://doi.org/10.1007/978-3-8348-8661-3

  • Publisher: Vieweg+Teubner Verlag Wiesbaden

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 2012

  • Softcover ISBN: 978-3-8348-1576-7Published: 10 October 2011

  • eBook ISBN: 978-3-8348-8661-3Published: 21 October 2011

  • Edition Number: 1

  • Number of Pages: VIII, 272

  • Number of Illustrations: 21 b/w illustrations

  • Topics: Analysis

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