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: Differentiable Manifolds
    sub title: A Theoretical Physics Approach
  name:
    name part: Torres del Castillo, Gerardo F.
    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: 2012
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VIII, 275 p. 20 illus. online resource.
  abstract: This textbook gives a concise introduction to the theory of differentiable manifolds, focusing on their applications to differential equations, differential geometry, and Hamiltonian mechanics. The work’s first three chapters introduce the basic concepts of the theory, such as differentiable maps, tangent vectors, vector and tensor fields, differential forms, local one-parameter groups of diffeomorphisms, and Lie derivatives. These tools are subsequently employed in the study of differential equations (Chapter 4), connections (Chapter 5), Riemannian manifolds (Chapter 6), Lie groups (Chapter 7), and Hamiltonian mechanics (Chapter 8). Throughout, the book contains examples, worked out in detail, as well as exercises intended to show how the formalism is applied to actual computations and to emphasize the connections among various areas of mathematics. Differentiable Manifolds is addressed to advanced undergraduate or beginning graduate students in mathematics or physics. Prerequisites include multivariable calculus, linear algebra, differential equations, and (for the last chapter) a basic knowledge of analytical mechanics.
  table of contents: Preface.-1 Manifolds.- 2 Lie Derivatives -- 3 Differential Forms -- 4 Integral Manifolds -- 5 Connections -- 6. Riemannian Manifolds -- 7 Lie Groups -- 8 Hamiltonian Classical Mechanics -- References.-Index.
  note: by Gerardo F. Torres del Castillo.
  subject:
    topic: Mathematics
  subject:
    topic: Topological groups
  subject:
    topic: Lie groups
  subject:
    topic: Manifolds (Mathematics)
  subject:
    topic: Complex manifolds
  subject:
    topic: Physics
  subject:
    topic: Mechanics
  subject:
    topic: Mathematics
  subject:
    topic: Manifolds and Cell Complexes (incl. Diff.Topology)
  subject:
    topic: Mechanics
  subject:
    topic: Mathematical Methods in Physics
  subject:
    topic: Topological Groups, Lie Groups
  classification: QA613-613.8
  classification: QA613.6-613.66
  classification: 514.34
  related item:
    title info:
      title: Springer eBooks
  identifier: 9780817682712
  identifier: http://dx.doi.org/10.1007/978-0-8176-8271-2
  record info:
    record creation date: 111007
    record change date: 20151204144414.0
    record identifier: 978-0-8176-8271-2