The Cauchy Transform, Potential Theory and Conformal Mapping

Steven R. Bell (Purdue University, USA)

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English

Chapman & Hall/CRC
14 October 2024

Calculus & mathematical analysis; Applied mathematics; Computing: general; Computer science

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 (Purdue University USA)
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Edition: 2nd edition
Dimensions: Height: 234mm, Width: 156mm,
Weight: 453g
ISBN: 9781032927510
ISBN 10: 1032927518
Pages: 222
Publication Date: 14 October 2024
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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