Potential theory / Lester Helms.

Potential theory / Lester Helms.

Second edition.

9781447164227 electronic book
1447164229 electronic book
9781447164210

London : Springer, 2014.

©2014

English

1 online resource (xiv, 485 pages) : illustrations (some color).

10.1007/978-1-4471-6422-7 doi

QA404.7

515/.96

Potential Theory presents a clear path from calculus to classical potential theory and beyond, with the aim of moving the reader into the area of mathematical research as quickly as possible. The subject matter is developed from first principles using only calculus. Commencing with the inverse square law for gravitational and electromagnetic forces and the divergence theorem, the author develops methods for constructing solutions of Laplace's equation on a region with prescribed values on the boundary of the region. The latter half of the book addresses more advanced material aimed at those with the background of a senior undergraduate or beginning graduate course in real analysis. Starting with solutions of the Dirichlet problem subject to mixed boundary conditions on the simplest of regions, methods of morphing such solutions onto solutions of Poisson's equation on more general regions are developed using diffeomorphisms and the Perron-Wiener-Brelot method, culminating in application to Brownian motion. In this new edition, many exercises have been added to reconnect the subject matter to the physical sciences. This book will undoubtedly be useful to graduate students and researchers in mathematics, physics, and engineering.

Includes bibliographical references and index.

Access limited to authorized users.

Description based on online resource; title from PDF title page (SpringerLink, viewed Apr. 16, 2014).

Universitext.

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