Analytic Functions of a Complex Variable

David Raymond Curtiss

doi:10.5948/UPO9781614440024

The MAA is pleased to re-issue the early Carus Mathematical Monographs in ebook and print-on-demand formats. Readers with an interest in the history of the undergraduate curriculum or the history of a particular field will be rewarded by study of these very clear and approachable little volumes. The theory of functions of a complex variable has been developed by the efforts of thousands of workers through the last hundred years. To give even the briefest account of the present state of that theory in all its branches would be impossible within the limits of this book. What is attempted here is a presentation of fundamental principles with sufficient details of proof and discussion to avoid the style of a mere summary or synopsis. In various places there are indications of directions in which special portions of the subject branch off from the main stem. The reader is assumed to have an acquaintance with elementary differential and integral calculus. Without such knowledge one may, however, obtain some idea of the scope and purposes of the theory of functions from this monograph. Those should profit most who are familiar with more than the elements of the calculus.

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Analytic Functions of a Complex Variable

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Contents

Frontmatter
pp i-iv

PREFACE
pp v-vi

Contents
pp vii-x

CHAPTER I - ORIGIN AND APPLICATIONS OF THE THEORY
pp 1-5

CHAPTER II - COMPLEX NUMBERS
pp 6-17

CHAPTER III - REAL FUNCTIONS OF REAL VARIABLES
pp 18-42

CHAPTER IV - COMPLEX FUNCTIONS THAT HAVE DERIVATIVES
pp 43-59

CHAPTER V - APPLICATIONS IN GEOMETRY AND PHYSICS
pp 60-82

CHAPTER VI - INTEGRALS OF ANALYTIC FUNCTIONS
pp 83-105

CHAPTER VII - INFINITE SERIES
pp 106-130

CHAPTER VIII - SINGULARITIES OF SINGLE-VALUED ANALYTIC FUNCTIONS
pp 131-146

CHAPTER IX - ANALYTIC CONTINUATION. MANY-VALUED ANALYTIC FUNCTIONS
pp 147-170

INDEX
pp 171-173

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