Book:Christian Berg/Kompleks funktionsteori

This book is based on a set of notes written in 1990 by the author to be used at the basic course about holomorphic functions at the University of Copenhagen.

An English translation of this book is still used as teaching material at the university, as of 2012.

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The book can be downloaded as a PDF file from the University of Copenhagen for free.

Download the 2012 edition (in English).

Download the 2004 edition (in Danish).

Subject Matter

 * Complex Analysis

Contents

 * Forord
 * i: Introduktion
 * 1: Holomorfe funktioner
 * 2: Kurveintegraler og stamfunktioner
 * 3: Cauchys sætninger
 * 4: Anvendelser af Cauchys integralformel
 * 5: Argument. Logaritme. Potens.
 * 6: Nulpunkter og isolerede singulariteter
 * 7: Residuer og deres anvendelser
 * 8: Maksimumprincippet
 * A: Appendix
 * Litteraturliste
 * Symbolliste
 * Index