rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Potential Theory
  name:
    name part: Helms, Lester L.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxk
    date issued: 2014
    edition: 2nd ed. 2014.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIV, 485 p. 2 illus. online resource.
  abstract: 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.
  table of contents: Preliminaries -- Laplace’s Equation -- The Dirichlet Problem -- Green Functions -- Negligible Sets -- Dirichlet Problem for Unbounded Regions -- Energy -- Interpolation and Monotonicity -- Newtonian Potential -- Elliptic Operators -- Apriori Bounds -- Oblique Derivative Problem -- Application to Diffusion Processes.
  note: by Lester L. Helms.
  subject:
    topic: Mathematics
  subject:
    topic: Partial differential equations
  subject:
    topic: Potential theory (Mathematics)
  subject:
    topic: Probabilities
  subject:
    topic: Mathematics
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Potential Theory
  subject:
    topic: Probability Theory and Stochastic Processes
  classification: QA370-380
  classification: 515.353
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Universitext
  identifier: 9781447164227
  identifier: http://dx.doi.org/10.1007/978-1-4471-6422-7
  record info:
    record creation date: 140410
    record change date: 20151103125026.0
    record identifier: 978-1-4471-6422-7