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.
Innehållsförteckning
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
Om författaren
Professor Dr. Wolfgang Fischer, University of Bremen, Faculty 3 – Mathematics
Professor Dr. Ingo Lieb, University of Bonn, Mathematical Institute
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