Theory of Functions of a Complex Variable

ISBN-10: 082183780X

ISBN-13: 9780821837801

Edition: 2nd 2005 (Revised)

List price: $96.00
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Description: Theorems are presented in a logical way and are carefully proved, making this a most useful book for students. --Choice This magnificent textbook, translated from the Russian, was first published in 1965-1967. The book covers all aspects of the theory of functions of one complex variable. The chosen proofs give the student the best `feel' for the subject. The watchwords are clarity and straightforwardness. The author was a leading Soviet function-theorist: It is seldom that an expert of his stature puts himself so wholly at the service of the student. This book includes over 150 illustrations and 700 exercises.

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Book details

List price: $96.00
Edition: 2nd
Copyright year: 2005
Publisher: American Mathematical Society
Publication date: 5/17/2005
Binding: Hardcover
Pages: 1138
Size: 6.25" wide x 9.00" long x 3.00" tall
Weight: 4.246
Language: English

Basic Concepts
Introduction
Complex numbers
Sets and functions
Limits and continuity
Connectedness
Curves and domains
Infinity and stereographic projection
Homeomorphisms
Differentiation
Elementary Functions
Differentiation and the Cauchy-Riemann equations
Geometric interpretation of the derivative
Conformal mapping
Elementary entire functions
Elementary meromorphic functions
Elementary multiple-valued functions
Integration
Power Series
Rectifiable curves
Complex integrals
Cauchy's integral theorem
Cauchy's integral and related topics
Uniform convergence
Infinite products
Power series: rudiments
Power series: ramifications
Methods for expanding functions in Taylor series Volume II
Laurent Series
Calculus of Residues
Laurent's series
Isolated singular points
The calculus of residues and its applications
Inverse and implicit functions
Univalent functions
Harmonic and Subharmonic Functions
Basic properties of harmonic functions
Applications to fluid dynamics
Subharmonic functions
The Poisson-Jensen formula and related topics
Entire and Meromorphic Functions
Basic properties of entire functions
Infinite product and partial fraction expansions Volume III
Conformal Mapping
Approximation Theory
Conformal mapping: rudiments
Conformal mapping: ramifications
Approximation by rational functions and polynomials
Periodic and Elliptic Functions
Periodic meromorphic functions
Elliptic functions: Weierstrass' theory
Elliptic functions: Jacobi's theory
Riemann Surfaces
Analytic Continuation
Riemann surfaces
Analytic continuation
The symmetry principle and its applications
Bibliography
Index
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