**Introduction to the Theory of Functions of a Complex Variable**

Introduction to the Theory of Functions of a Complex Variable By E.T. Copson

Publisher: O U P 1955 | 456 Pages | ISBN: 0198531451 | DJVU | 3 MB

This book is based on courses of lectures given to undergraduates in the Universities of Edinburgh and St. Andrews, and is intended to provide an easy introduction to the methods of the theory of functions of a complex variable. The reader is assumed to have a knowledge of the elements of the theory of functions of a real variable, such as is contained, for example, in Hardy's Course of Pure Mathematics; an acquaintance with the easier parts of Bromwich's Infinite Series would prove advantageous, but is not essential.

The first six chapters contain an exposition, based on Cauchy's Theorem, of the properties of one-valued differcntiable functions of a complex variable. In the rest of the book the problem of conformal representation, the elements of the theory of integral functions and the behaviour of some of the special functions of analysis are discussed by the methods developed in the earlier part. The book concludes with the classical proof of Picard's Theorem.