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:
    non sort: The
    title: Calculus of Variations
  name:
    name part: Brunt, Bruce van.
    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: 2004
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIV, 292 p. online resource.
  abstract: Thecalculusofvariationshasalonghistoryofinteractionwithotherbranches of mathematics such as geometry and di?erential equations, and with physics, particularly mechanics. More recently, the calculus of variations has found applicationsinother?eldssuchaseconomicsandelectricalengineering. Much of the mathematics underlying control theory, for instance, can be regarded as part of the calculus of variations. This book is an introduction to the calculus of variations for mathema- cians and scientists. The reader interested primarily in mathematics will ?nd results of interest in geometry and di?erential equations. I have paused at times to develop the proofs of some of these results, and discuss brie?y v- ious topics not normally found in an introductory book on this subject such as the existence and uniqueness of solutions to boundary-value problems, the inverse problem, and Morse theory. I have made “passive use” of functional analysis (in particular normed vector spaces) to place certain results in c- text and reassure the mathematician that a suitable framework is available for a more rigorous study. For the reader interested mainly in techniques and applications of the calculus of variations, I leavened the book with num- ous examples mostly from physics. In addition, topics such as Hamilton’s Principle, eigenvalue approximations, conservation laws, and nonholonomic constraints in mechanics are discussed. More importantly, the book is written on two levels. The technical details for many of the results can be skipped on the initial reading. The student can thus learn the main results in each chapter and return as needed to the proofs for a deeper understanding.
  table of contents: The First Variation -- Some Generalizations -- Isoperimetric Problems -- Applications to Eigenvalue Problems -- Holonomic and Nonholonomic Constraints -- Problems with Variable Endpoints -- The Hamiltonian Formulation -- Noether’s Theorem -- The Second Variation.
  note: by Bruce van Brunt.
  subject:
    topic: Mathematics
  subject:
    topic: Calculus of variations
  subject:
    topic: Mathematics
  subject:
    topic: Calculus of Variations and Optimal Control; Optimization
  classification: QA315-316
  classification: QA402.3
  classification: QA402.5-QA402.6
  classification: 515.64
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Universitext
  identifier: 9780387216973
  identifier: http://dx.doi.org/10.1007/b97436
  record info:
    record creation date: 100301
    record change date: 20151125022034.0
    record identifier: 978-0-387-21697-3