Potential Theory (Universitext) 2nd Edition by Lester L. Helms (PDF)

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐There are at least two sorts of books in advanced mathematics. Some books are written to advance the authors’ carrier, to be cited in bibliographics, or to satisfy the author who feels flattered by the sad fact that the novice has no access to the knowledge. The learner will never understand anything from the book anyway.Some books are written for the learner to read and learn from them. Helms’s book is in this second category. If you are serious and want to study the classical potential theory, you should read this book. It is very accessible, and the proofs are detailed. I have a copy of the old edition (1969) and a copy of the new one, which covers more materials, and I find them enjoyable to read.

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