ENGLISH

Potential Theory

By Lester L. Helms (auth.)

Book information

Publisher
Springer-Verlag London
Year
2014
ISBN
978-1-4471-6421-0, 978-1-4471-6422-7
DOI
10.1007/978-1-4471-6422-7
Language
english
Format
PDF
Filesize
5 MB (4809843 bytes)
Series
Universitext
Edition
2
Pages
485\494
Time added
2014-06-12 06:00:00
Partial Differential Equations; Potential Theory;

Description

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.

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