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A Course in Complex Analysis

From Basic Results to Advanced Topics

  • Wolfgang Fischer
  • Ingo Lieb

Table of contents

  1. Front Matter
    Pages i-viii
  2. Wolfgang Fischer, Ingo Lieb
    Pages 1-35
  3. Wolfgang Fischer, Ingo Lieb
    Pages 36-70
  4. Wolfgang Fischer, Ingo Lieb
    Pages 71-107
  5. Wolfgang Fischer, Ingo Lieb
    Pages 108-147
  6. Wolfgang Fischer, Ingo Lieb
    Pages 148-192
  7. Wolfgang Fischer, Ingo Lieb
    Pages 193-213
  8. Wolfgang Fischer, Ingo Lieb
    Pages 214-257
  9. Back Matter
    Pages 258-272

About this book

Introduction

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.

Content
Analysis in the complex plane - The fundamental theorems of complex analysis - Functions on the plane and on the sphere - Integral formulas, residues and applications - Non-elementary functions - Meromorphic functions of several variables - Holomorphic maps: Geometric aspects

Readership
Advanced undergraduates (bachelor students) and beginning graduate students (master's programme)
Lecturers in mathematics
About the authors
Professor Dr. Ingo Lieb, Department of Mathematics, University of Bonn
Professor Dr. Wolfgang Fischer, Department of Mathematics, University of Bremen

Keywords

Complex Analysis Functions of complex numbers Funktionentheorie Holomorphic Functions Komplexe Analysis

Authors and affiliations

  • Wolfgang Fischer
    • 1
  • Ingo Lieb
    • 2
  1. 1.Faculty 3 - MathematicsUniversity of BremenBremenGermany
  2. 2.Mathematical InstituteUniversity of BonnBonnGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-8348-8661-3
  • Copyright Information Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 2012
  • Publisher Name Vieweg+Teubner Verlag
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-8348-1576-7
  • Online ISBN 978-3-8348-8661-3
  • Buy this book on publisher's site
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