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: An
    title: Introduction to Differential Manifolds
  name:
    name part: Lafontaine, Jacques.
    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: 2015
    edition: 1st ed. 2015.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIX, 395 p. 49 illus. online resource.
  abstract: This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of “abstract” notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergraduate and graduate students for a first contact to differential manifolds, mathematicians from other fields and physicists who wish to acquire some feeling about this beautiful theory. The original French text Introduction aux variétés différentielles has been a best-seller in its category in France for many years. Jacques Lafontaine was successively assistant Professor at Paris Diderot University and Professor at the University of Montpellier, where he is presently emeritus. His main research interests are Riemannian and pseudo-Riemannian geometry, including some aspects of mathematical relativity. Besides his personal research articles, he was involved in several textbooks and research monographs.
  table of contents: Differential Calculus -- Manifolds: The Basics -- From Local to Global -- Lie Groups -- Differential Forms -- Integration and Applications -- Cohomology and Degree Theory -- Euler-Poincaré and Gauss-Bonnet.
  note: by Jacques Lafontaine.
  subject:
    topic: Mathematics
  subject:
    topic: Differential geometry
  subject:
    topic: Mathematics
  subject:
    topic: Differential Geometry
  classification: QA641-670
  classification: 516.36
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783319207353
  identifier: http://dx.doi.org/10.1007/978-3-319-20735-3
  record info:
    record creation date: 150729
    record change date: 20151204174943.0
    record identifier: 978-3-319-20735-3