Translations of Mathematical Monographs 1992; 303 pp; hardcover Volume: 106 ISBN10: 0821845624 ISBN13: 9780821845622 List Price: US$122 Member Price: US$97.60 Order Code: MMONO/106
 This book presents a systematic exposition of the theory of conformal mappings, boundary value problems for analytic and harmonic functions, and the relationship between the two subjects. It is suitable for use as an undergraduate or graduate level textbook, and exercises are included. The first three chapters recount existence and uniqueness theorems of conformal mappings from simply and multiply connected domains to standard domains, some properties of analytic functions, harmonic functions and schlicht meromorphic functions, and representations of conformal mappings. In the remaining three chapters, the basic boundary value problems for analytic and harmonic functions are discussed in detail, including some new methods and results obtained by the author. For example, the RiemannHilbert boundary value problem with piecewise continuous coefficients in a multiply connected domain is covered in chapter five, and some irregular oblique derivative problems are treated in chapter six. Readership Graduate students as well as experts in theoretical and mathematical physics, differential and integral equations and mathematical analysis. Reviews "The exposition is clear and very detailed ... most constructive methods are described in detail while in the proofs of theorems every step is made explicitly. Moreover at the end of each chapter a series of exercises is provided, allowing the reader to check his/her understanding of the preceeding chapter."  mededelingen van het wiskundig genootschap "Suitable for use as an undergraduate or graduate level textbook."  Zentralblatt MATH Table of Contents  Some properties of analytic and harmonic functions
 Conformal mappings of simply connected domains
 Conformal mappings of multiply connected domains
 Applications of integrals of Cauchy type to boundary value problems
 The Hilbert boundary value problem for analytic functions on multiply connected domains
 Basic boundary value problems for harmonic functions
 Appendix 1. A brief introduction to quasiconformal mappings
 Appendix 2. Some connections between integral equations and boundary value problems
