Hardcover ISBN:  9780821845622 
Product Code:  MMONO/106 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445171 
Product Code:  MMONO/106.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821845622 
eBook: ISBN:  9781470445171 
Product Code:  MMONO/106.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 
Hardcover ISBN:  9780821845622 
Product Code:  MMONO/106 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445171 
Product Code:  MMONO/106.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821845622 
eBook ISBN:  9781470445171 
Product Code:  MMONO/106.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 106; 1992; 303 ppMSC: Primary 30; 47; Secondary 81
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.
ReadershipGraduate students as well as experts in theoretical and mathematical physics, differential and integral equations and mathematical analysis.

Table of Contents

Chapters

Chapter 1. Some properties of analytic and harmonic functions

Chapter 2. Conformal mappings of simply connected domains

Chapter 3. Conformal mappings of multiply connected domains

Chapter 4. Applications of integrals of Cauchy type to boundary value problems

Chapter 5. The Hilbert boundary value problem for analytic functions on multiply connected domains

Chapter 6. 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


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


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Reviews
 Requests
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.
Graduate students as well as experts in theoretical and mathematical physics, differential and integral equations and mathematical analysis.

Chapters

Chapter 1. Some properties of analytic and harmonic functions

Chapter 2. Conformal mappings of simply connected domains

Chapter 3. Conformal mappings of multiply connected domains

Chapter 4. Applications of integrals of Cauchy type to boundary value problems

Chapter 5. The Hilbert boundary value problem for analytic functions on multiply connected domains

Chapter 6. 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

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