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: A
    title: Geometric Approach to Differential Forms
  name:
    name part: Bachman, 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: 2006
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVI, 133 p. 39 illus. online resource.
  abstract: The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the undergraduate level. The book begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The author approaches the subject with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. This facilitates the development of differential forms without assuming a background in linear algebra. Throughout the text, emphasis is placed on applications in 3 dimensions, but all definitions are given so as to be easily generalized to higher dimensions. A centerpiece of the text is the generalized Stokes' theorem. Although this theorem implies all of the classical integral theorems of vector calculus, it is far easier for students to both comprehend and remember. The text is designed to support three distinct course tracks: the first as the primary textbook for third semester (multivariable) calculus, suitable for anyone with a year of calculus; the second is aimed at students enrolled in vector calculus; while the third targets advanced undergraduates and beginning graduate students in physics or mathematics, touching on more advanced topics such as Maxwell's equations, foliation theory, and cohomology. Containing excellent motivation, numerous illustrations and solutions to selected problems in an appendix, the material has been tested in the classroom along all three potential course tracks.
  table of contents: Multivariable Calculus -- Parameterizations -- to Forms -- Forms -- Differential Forms -- Differentiation of Forms -- Stokes’ Theorem -- Applications -- Manifolds.
  note: by David Bachman.
  subject:
    topic: Mathematics
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: Manifolds (Mathematics)
  subject:
    topic: Functions of real variables
  subject:
    topic: Differential geometry
  subject:
    topic: Mathematics
  subject:
    topic: Global Analysis and Analysis on Manifolds
  subject:
    topic: Real Functions
  subject:
    topic: Differential Geometry
  classification: QA614-614.97
  classification: 514.74
  related item:
    title info:
      title: Springer eBooks
  identifier: 9780817645205
  identifier: http://dx.doi.org/10.1007/978-0-8176-4520-5
  record info:
    record creation date: 100301
    record change date: 20151204190938.0
    record identifier: 978-0-8176-4520-5