Cauchy Transform Potential Theory and Conformal Mapping

<p><strong>The Cauchy Transform Potential Theory and Conformal Mapping</strong> 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.</p><p>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. </p><p>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. </p><p>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. </p><p>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.</p>