Theory of Functions of a Complex Variable

Name: Theory of Functions of a Complex Variable
Price: 55.05 USD
Availability: InStock
ISBN: 9780821837801

ISBN-10: 082183780X

ISBN-13: 9780821837801

Edition: 2nd 2005 (Revised)

Authors: A. I. Markushevich, Richard A. Silverman

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.

Book details

List price: $96.00
Edition: 2nd
Copyright year: 2005
Publisher: American Mathematical Society
Publication date: 5/30/2005
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