AMS Chelsea Publishing 1977; 1138 pp; hardcover Volume: 296 Reprint/Revision History: reprinted 2005, 2014 ISBN10: 082183780X ISBN13: 9780821837801 List Price: US$96 Member Price: US$86.40 Order Code: CHEL/296.H
 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 19651967. 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 functiontheorist: 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. Table of Contents Volume I, Part 1: Basic Concepts  I.1 Introduction
 I.2 Complex numbers
 I.3 Sets and functions. Limits and continuity
 I.4 Connectedness. Curves and domains
 I.5. Infinity and stereographic projection
 I.6 Homeomorphisms
Part 2: Differentiation. Elementary Functions  I.7 Differentiation and the CauchyRiemann equations
 I.8 Geometric interpretation of the derivative. Conformal mapping
 I.9 Elementary entire functions
 I.10 Elementary meromorphic functions
 I.11 Elementary multiplevalued functions
Part 3: Integration. Power Series  I.12 Rectifiable curves. Complex integrals
 I.13 Cauchy's integral theorem
 I.14 Cauchy's integral and related topics
 I.15 Uniform convergence. Infinite products
 I.16 Power series: Rudiments
 I.17 Power series: Ramifications
 I.18 Methods for expanding functions in Taylor series
Volume II, Part 1: Laurent Series. Calculus of Residues  II.1 Laurent's series. Isolated singular points
 II.2 The calculus of residues and its applications
 II.3 Inverse and implicit functions
 II.4 Univalent functions
Part 2: Harmonic and Subharmonic Functions  II.5 Basic properties of harmonic functions
 II.6 Applications to fluid dynamics
 II.7 Subharmonic functions
 II.8 The PoissonJensen formula and related topics
Part 3: Entire and Meromorphic Functions  II.9 Basic properties of entire functions
 II.10 Infinite product and partial fraction expansions
Volume III, Part 1: Conformal Mapping. Approximation Theory  III.1 Conformal mapping: Rudiments
 III.2 Conformal mapping: Ramifications
 III.3 Approximation by rational functions and polynomials
Part 2: Periodic and Elliptic Functions  III.4 Periodic meromorphic functions
 III.5 Elliptic functions: Weierstrass' theory
 III.6 Elliptic functions: Jacobi's theory
Part 3: Riemann Surfaces. Analytic Continuation  III.7 Riemann surfaces
 III.8 Analytic continuation
 III.9 The symmetry principle and its applications
 Bibliography
 Index
