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Theory of Functions of a Complex Variable, Volume 1

C. Caratheodory
Publisher: 
American Mathematical Society/Chelsea
Publication Date: 
2001
Number of Pages: 
304
Format: 
Hardcover
Price: 
41.00
ISBN: 
978-0821828311
Category: 
Textbook
BLL Rating: 

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

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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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