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$43 Member Price: US$38.70 Order Code: CHEL/97.H
![[Add Item]](/images/addtocart.gif) | 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 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
 |
