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Theory of Functions of a Complex Variable, Volume 1
C. Carathéodory

AMS Chelsea Publishing
1954; 304 pp; hardcover
Volume: 97
Reprint/Revision History:
First AMS printing 2001
ISBN-10: 0-8218-2831-2
ISBN-13: 978-0-8218-2831-1
List Price: US$46
Member Price: US$41.40
Order Code: CHEL/97.H
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This book is a translation by F. Steinhardt of the last of Carathéodory's celebrated text books, Funktiontheorie, Volume 1.


"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 non-Euclidean 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 maximum-modulus 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
  • Partial-fraction 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
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