AMS Chelsea Publishing 1954; 304 pp; hardcover Volume: 97 Reprint/Revision History: First AMS printing 2001 ISBN10: 0821828312 ISBN13: 9780821828311 List Price: US$43 Member Price: US$38.70 Order Code: CHEL/97.H
 This book is a translation by F. Steinhardt of the last of Carathéodory's celebrated text books, Funktiontheorie, Volume 1. 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 Table of Contents Part One: Complex Numbers  The complex numbers from the algebraic point of view
 The geometry of the complex numbers
 Euclidean, spherical, and nonEuclidean geometry
Part Two: Some Results From Point Set Theory and From Topology  Convergent sequences of numbers and continuous complex functions
 Curves and regions
 Contour integration
Part Three: Analytic Functions  Foundations of the theory
 The maximummodulus principle
 The Poisson integral and harmonic functions
 Meromorphic functions
Part Four: Analytic Functions Defined By Limiting Processes  Continuous convergence
 Normal families of meromorphic functions
 Power series
 Partialfraction decomposition and the calculus of residues
Part Five: Special Functions  The exponential and trigonometric functions
 The logarithmic function and the general power function
 The Bernoulli numbers and the gamma function
 Index
