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: Differential Equations: Theory and Applications
  name:
    name part: Betounes, David.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2010
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIV, 626 p. online resource.
  abstract: The book provides a comprehensive introduction to the theory of ordinary differential equations at the graduate level and includes applications to Newtonian and Hamiltonian mechanics. It not only has a large number of examples and computer graphics, but also has a complete collection of proofs for the major theorems, ranging from the usual existence and uniqueness results to the Hartman-Grobman linearization theorem and the Jordan canonical form theorem. The book can be used almost exclusively in the traditional way for graduate math courses, or it can be used in an applied way for interdisciplinary courses involving physics, engineering, and other science majors. For this reason an extensive computer component using Maple is provided on Springer’s website. This new edition has been extensively revised throughout, particularly the chapters on linear systems, stability theory and Hamiltonian systems. The computer component is an in-depth supplement and complement to the material in the text and contains an introduction to discrete dynamical systems and iterated maps, special-purpose Maple code for animating phase portraits, stair diagrams, N-body motions, and rigid-body motions, and numerous tutorial Maple worksheets pertaining to all aspects of using Maple to study the topics in the text. Review from first edition: "This book is intended for first- and second- year graduate students in mathematics and also organized to be used for interdisciplinary courses in applied mathematics, physics, and engineering. ... The book is well written and provides many interesting examples. The author gives a comprehensive introduction to the theory on ordinary differential equations with a focus on mechanics and dynamical systems. The exposition is clear and easily understood...." (Yuan Rong, Zentralblatt MATH, Vol. 993 (18), 2002).
  table of contents: Techniques, Concepts and Examples -- Existence and Uniqueness: The Flow Map -- Linear Systems -- Linearization #x0026; Transformation -- Stability Theory -- Integrable Systems -- Newtonian Mechanics -- Hamiltonian Systems -- Elementary Analysis -- Lipschitz Maps and Linearization -- Linear Algebra -- Electronic Contents.
  note: by David Betounes.
  subject:
    topic: Mathematics
  subject:
    topic: Dynamics
  subject:
    topic: Ergodic theory
  subject:
    topic: Differential equations
  subject:
    topic: Numerical analysis
  subject:
    topic: Physics
  subject:
    topic: Mathematics
  subject:
    topic: Ordinary Differential Equations
  subject:
    topic: Numerical Analysis
  subject:
    topic: Dynamical Systems and Ergodic Theory
  subject:
    topic: Mathematical Methods in Physics
  classification: QA372
  classification: 515.352
  related item:
    title info:
      title: Springer eBooks
  identifier: 9781441911636
  identifier: http://dx.doi.org/10.1007/978-1-4419-1163-6
  record info:
    record creation date: 100301
    record change date: 20151111121157.0
    record identifier: 978-1-4419-1163-6