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: Introduction to Partial Differential Equations
  name:
    name part: Olver, Peter J.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2014
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXV, 636 p. 143 illus. online resource.
  abstract: This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solitons, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements. Peter J. Olver is professor of mathematics at the University of Minnesota. His wide-ranging research interests are centered on the development of symmetry-based methods for differential equations and their manifold applications. He is the author of over 130 papers published in major scientific research journals as well as 4…
  table of contents: What are Partial Differential Equations? -- Linear and Nonlinear Waves -- Fourier Series -- Separation of Variables -- Finite Differences -- Generalized Functions and Green’s Functions -- Complex Analysis and Conformal Mapping -- Fourier Transforms -- Linear and Nonlinear Evolution Equations -- A General Framework for Linear Partial Differential Equations -- Finite Elements and Weak Solutions -- Dynamics of Planar Media -- Partial Differential Equations in Space .
  note: by Peter J. Olver.
  subject:
    topic: Mathematics
  subject:
    topic: Fourier analysis
  subject:
    topic: Partial differential equations
  subject:
    topic: System theory
  subject:
    topic: Mathematics
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Complex Systems
  subject:
    topic: Fourier Analysis
  classification: QA370-380
  classification: 515.353
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Undergraduate Texts in Mathematics
  identifier: 9783319020990
  identifier: http://dx.doi.org/10.1007/978-3-319-02099-0
  record info:
    record creation date: 131108
    record change date: 20170228143039.0
    record identifier: 978-3-319-02099-0