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: New Approach to Differential Geometry using Clifford's Geometric Algebra
  name:
    name part: Snygg, John.
    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: XVII, 465 p. 102 illus. online resource.
  abstract: Differential geometry is the study of curvature and calculus of curves and surfaces. Because of an historical accident, the Geometric Algebra devised by William Kingdom Clifford (1845–1879) has been overlooked in favor of the more complicated and less powerful formalism of differential forms and tangent vectors to deal with differential geometry. Fortuitously a student who has completed an undergraduate course in linear algebra is better prepared to deal with the intricacies of Clifford algebra than with the formalism currently used. Clifford algebra enables one to demonstrate a close relation between curvature and certain rotations. This is an advantage both conceptually and computationally—particularly in higher dimensions. Key features and topics include: * a unique undergraduate-level approach to differential geometry; * brief biographies of historically relevant mathematicians and physicists; * some aspects of special and general relativity accessible to undergraduates with no knowledge of Newtonian physics; * chapter-by-chapter exercises. The textbook will also serve as a useful classroom resource primarily for undergraduates as well as beginning-level graduate students; researchers in the algebra and physics communities may also find the book useful as a self-study guide.
  table of contents: Preface -- Introduction -- Clifford Algebra in Euclidean 3-Space -- Clifford Algebra in Minkowski 4-Space -- Clifford Algebra in Flat n-Space -- Curved Spaces -- The Gauss-Bonnet Formula -- Non-Euclidean (Hyperbolic) Geometry -- Some Extrinsic Geometry in E^n -- Ruled Surfaces Continued -- Lines of Curvature -- Minimal Surfaces -- Some General Relativity -- Matrix Representation of a Clifford Algebra -- Construction of Coordinate Dirac Matrices -- A Few Terms of the Taylor's Series for the Urdī-Copernican Model for the Outer Planets -- A Few Terms of the Taylor's Series for Kepler's Orbits -- References -- Index.
  note: by John Snygg.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Applied mathematics
  subject:
    topic: Engineering mathematics
  subject:
    topic: Differential geometry
  subject:
    topic: Mathematical physics
  subject:
    topic: Physics
  subject:
    topic: Mathematics
  subject:
    topic: Differential Geometry
  subject:
    topic: Mathematical Methods in Physics
  subject:
    topic: Mathematical Physics
  subject:
    topic: Mathematics, general
  subject:
    topic: Algebra
  subject:
    topic: Applications of Mathematics
  classification: QA641-670
  classification: 516.36
  related item:
    title info:
      title: Springer eBooks
  identifier: 9780817682835
  identifier: http://dx.doi.org/10.1007/978-0-8176-8283-5
  record info:
    record creation date: 111207
    record change date: 20151204173157.0
    record identifier: 978-0-8176-8283-5