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Theory of Functions of a Complex Variable, Vol 1
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
eBook ISBN:  9781470440756 
Product Code:  CHEL/97.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
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Theory of Functions of a Complex Variable, Vol 1
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
eBook ISBN:  9781470440756 
Product Code:  CHEL/97.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 

Book DetailsAMS Chelsea PublishingVolume: 97; 1954; 304 ppMSC: Primary 30; 01;
This book is a translation by F. Steinhardt of the last of Carathéodory's celebrated text books, Funktiontheorie, Volume 1.

Table of Contents

Front Cover

Title page

Copyright

Translator’s preface

Editor’s preface

Author’s preface

Contents

Part One: Complex numbers

Chapter I. The complex numbers from the algebraic point of view

Chapter II. The geometry of the complex numbers

Chapter III. Euclidean, spherical, and nonEuclidean geometry

Part Two: Some results from point set theory and from topology

Chapter I. Convergent sequences of numbers and continuous complex functions

Chapter II. Curves and regions

Chapter III. Contour integration

Part Three: Analytic functions

Chapter I. Foundations of the theory

Chapter II. The maximummodulus principle

Chapter III. The Poisson integral and harmonic functions

Chapter IV. Meromorphic functions

Part Four: Analytic functions defined by limiting processes

Chapter I. Continuous convergence

Chapter II. Normal families of meromorphic functions

Chapter III. Power series

Chapter IV. Partialfraction decomposition and the calculus of residues

Part Five: Special functions

Chapter I. The exponential and trigonometric functions

Chapter II. The logarithmic function and the general power function

Chapter III. The Bernoulli numbers and the gamma function

Index

Untitled


Additional Material

Reviews

A book by a master ... Carathéodory himself regarded [it] as his finest achievement ... written from a catholic point of view.
Bulletin of the AMS


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
Volume: 97; 1954; 304 pp
MSC: Primary 30; 01;
This book is a translation by F. Steinhardt of the last of Carathéodory's celebrated text books, Funktiontheorie, Volume 1.

Front Cover

Title page

Copyright

Translator’s preface

Editor’s preface

Author’s preface

Contents

Part One: Complex numbers

Chapter I. The complex numbers from the algebraic point of view

Chapter II. The geometry of the complex numbers

Chapter III. Euclidean, spherical, and nonEuclidean geometry

Part Two: Some results from point set theory and from topology

Chapter I. Convergent sequences of numbers and continuous complex functions

Chapter II. Curves and regions

Chapter III. Contour integration

Part Three: Analytic functions

Chapter I. Foundations of the theory

Chapter II. The maximummodulus principle

Chapter III. The Poisson integral and harmonic functions

Chapter IV. Meromorphic functions

Part Four: Analytic functions defined by limiting processes

Chapter I. Continuous convergence

Chapter II. Normal families of meromorphic functions

Chapter III. Power series

Chapter IV. Partialfraction decomposition and the calculus of residues

Part Five: Special functions

Chapter I. The exponential and trigonometric functions

Chapter II. The logarithmic function and the general power function

Chapter III. The Bernoulli numbers and the gamma function

Index

Untitled

A book by a master ... Carathéodory himself regarded [it] as his finest achievement ... written from a catholic point of view.
Bulletin of the AMS
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.