eBook ISBN:  9781614440024 
Product Code:  CAR/2.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 
eBook ISBN:  9781614440024 
Product Code:  CAR/2.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 

Book DetailsThe Carus Mathematical MonographsVolume: 2; 1926; 173 pp
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 who are familiar with more than the elements of the calculus should profit most.

Table of Contents

Chapters

Chapter I. Origin and applications of the theory

Chapter II. Complex numbers

Chapter III. Real functions of real variables

Chapter IV. Complex functions that have derivatives

Chapter V. Applications in geometry and physics

Chapter VI. Integrals of analytic functions

Chapter VII. Infinite series

Chapter VIII. Singularities of singlevalued analytic functions

Chapter IX. Analytic Continuation. ManyValued Analytic Functions


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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 who are familiar with more than the elements of the calculus should profit most.

Chapters

Chapter I. Origin and applications of the theory

Chapter II. Complex numbers

Chapter III. Real functions of real variables

Chapter IV. Complex functions that have derivatives

Chapter V. Applications in geometry and physics

Chapter VI. Integrals of analytic functions

Chapter VII. Infinite series

Chapter VIII. Singularities of singlevalued analytic functions

Chapter IX. Analytic Continuation. ManyValued Analytic Functions