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

✍ Scribed by Prof. Dr. Wolfgang Fischer, Prof. Dr. Ingo Lieb (auth.)

• Publisher: Vieweg+Teubner Verlag
• Year: 2012
• Tongue: English
• Leaves: 279
• Edition: 1
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Front Matter....Pages i-viii
Analysis in the complex plane....Pages 1-35
The fundamental theorems of complex analysis....Pages 36-70
Functions on the plane and on the sphere....Pages 71-107
Integral formulas, residues, and applications....Pages 108-147
Non-elementary functions....Pages 148-192
Meromorphic functions of several variables....Pages 193-213
Holomorphic maps: Geometric aspects....Pages 214-257
Back Matter....Pages 258-272

✦ Subjects

Analysis