Universitext

Potential Theory

Authors: Helms, Lester L.

  • Shows how solutions are morphed into local solutions on regions with curved boundaries
  • Discusses the connection between potential theory and Brownian motion
  • Introduces all the important concepts of classical potential theory
  • Equips readers for further study in elliptic partial differential equations, axiomatic potential theory and the interplay between probability theory and potential theory
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eBook $59.99
price for USA (gross)
  • ISBN 978-1-4471-6422-7
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  • Immediate eBook download after purchase
Softcover $79.99
price for USA
  • ISBN 978-1-4471-6421-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
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About this Textbook

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.

About the authors

The author's interests lie in three interrelated topics: heat equations associated with second-order elliptic operators, Markov or diffusion processes and potential theory.

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Table of contents (13 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4471-6422-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA
  • ISBN 978-1-4471-6421-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Potential Theory
Authors
Series Title
Universitext
Copyright
2014
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-1-4471-6422-7
DOI
10.1007/978-1-4471-6422-7
Softcover ISBN
978-1-4471-6421-0
Series ISSN
0172-5939
Edition Number
2
Number of Pages
XIV, 485
Number of Illustrations and Tables
2 b/w illustrations
Topics