The Cauchy Transform Potential Theory and Conformal Mapping (Studies in Advanced Mathematics)

Steven R. Bell

ISBN 10: 084938270X / ISBN 13: 9780849382703

Published by CRC Press, 1992

About this Item

A very good hardcover copy which does not appear to have been used. No markings. No dust jacket, as issued.

Seller Inventory # mon0000682948

Bibliographic Details

• Title: The Cauchy Transform Potential Theory and Conformal Mapping (Studies in Advanced Mathematics)
• Publisher: CRC Press
• Publication Date: 1992
• Language: English
• ISBN 10: 084938270X
• ISBN 13: 9780849382703
• Binding: hardcover
• Condition: Very Good

About this title

Synopsis

The Cauchy integral formula is the most central result in all of classical function theory. A recent discovery of Kerzman and Stein allows more theorems than ever to be deduced from simple facts about the Cauchy integral. In this book, the Riemann Mapping Theorem is deduced, the Dirichlet and Neumann problems for the Laplace operator are solved, the Poisson kernal is constructed, and the inhomogenous Cauchy-Reimann equations are solved concretely using formulas stemming from the Kerzman-Stein result. These explicit formulas yield new numerical methods for computing the classical objects of potential theory and conformal mapping, and the book provides succinct, complete explanations of these methods. The Cauchy Transform, Potential Theory, and Conformal Mapping is suitable for pure and applied math students taking a beginning graduate-level topics course on aspects of complex analysis. It will also be useful to physicists and engineers interested in a clear exposition on a fundamental topic of complex analysis, methods, and their application.