The Cauchy Transform, Potential Theory and Conformal Mapping

Steven R. Bell

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English

Chapman & Hall/CRC
23 November 2015

Number systems; Calculus & mathematical analysis; Applied mathematics

The Cauchy Transform, Potential Theory and Conformal Mapping explores the most central result in all of classical function theory, the Cauchy integral formula, in a new and novel way based on an advance made by Kerzman and Stein in 1976.

The book provides a fast track to understanding the Riemann Mapping Theorem. The Dirichlet and Neumann problems for the Laplace operator are solved, the Poisson kernel is constructed, and the inhomogenous Cauchy-Reimann equations are solved concretely and efficiently 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.

Four new chapters have been added to this second edition: two on quadrature domains and another two on complexity of the objects of complex analysis and improved Riemann mapping theorems.

The book is suitable for pure and applied math students taking a beginning graduate-level topics course on aspects of complex analysis as well as physicists and engineers interested in a clear exposition on a fundamental topic of complex analysis, methods, and their application.

By: Steven R. Bell
Imprint: Chapman & Hall/CRC
Country of Publication: United States
Edition: 2nd edition
Dimensions: Height: 234mm, Width: 156mm, Spine: 18mm
Weight: 450g
ISBN: 9781498727204
ISBN 10: 1498727204
Pages: 209
Publication Date: 23 November 2015
Audience: College/higher education , College/higher education , A / AS level , Primary
Format: Hardback
Publisher's Status: Active

Steven R. Bell, PhD, professor, Department of Mathematics, Purdue University, West Lafayette, Indiana, USA, and Fellow of the AMS