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.

Hersteller:
Springer Vieweg in Springer Science + Business Media
juergen.hartmann@springer.com
Abraham-Lincoln-Straße 46
DE 65189 Wiesbaden

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

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

Complex Analysis for Bachelor and Master Studies