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: Differential forms
    sub title: theory and practice
  name:
    name part: Weintraub, Steven H.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: ScienceDirect (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: enk
    date issued: 2014
    edition: Second edition.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource
  abstract: Differential forms are utilized as a mathematical technique to help students, researchers, and engineers analyze and interpret problems where abstract spaces and structures are concerned, and when questions of shape, size, and relative positions are involved. Differential Forms has gained high recognition in the mathematical and scientific community as a powerful computational tool in solving research problems and simplifying very abstract problems through mathematical analysis on a computer. Differential Forms, 2nd Edition, is a solid resource for students and prof.
  table of contents: Half Title; Title Page; Copyright; Dedication; Contents; Preface; 1 Differential Forms in Rn, I; 1.0 Euclidean spaces, tangent spaces, and tangent vector fields; 1.1 The algebra of differential forms; 1.2 Exterior differentiation; 1.3 The fundamental correspondence; 1.4 The Converse of Poincaré's Lemma, I; 1.5 Exercises; 2 Differential Forms in Rn, II; 2.1 1-Forms; 2.2 k-Forms; 2.3 Orientation and signed volume; 2.4 The converse of Poincaré's Lemma, II; 2.5 Exercises; 3 Push-forwards and Pull-backs in Rn; 3.1 Tangent vectors; 3.2 Points, tangent vectors, and push-forwards.
  table of contents: 3.3 Differential forms and pull-backs3.4 Pull-backs, products, and exterior derivatives; 3.5 Smooth homotopies and the Converse of Poincaré's Lemma, III; 3.6 Exercises; 4 Smooth Manifolds; 4.1 The notion of a smooth manifold; 4.2 Tangent vectors and differential forms; 4.3 Further constructions; 4.4 Orientations of manifolds'227intuitive discussion; 4.5 Orientations of manifolds'227careful development; 4.6 Partitions of unity; 4.7 Smooth homotopies and the Converse of Poincaré's Lemma in general; 4.8 Exercises; 5 Vector Bundles and the Global Point of View.
  table of contents: 5.1 The definition of a vector bundle5.2 The dual bundle, and related bundles; 5.3 The tangent bundle of a smooth manifold, and related bundles; 5.4 Exercises; 6 Integration of Differential Forms; 6.1 Definite integrals in textmathbbRn; 6.2 Definition of the integral in general; 6.3 The integral of a 0-form over a point; 6.4 The integral of a 1-form over a curve; 6.5 The integral of a 2-form over a surface; 6.6 The integral of a 3-form over a solid body; 6.7 Chains and integration on chains; 6.8 Exercises; 7 The Generalized Stokes's Theorem; 7.1 Statement of the theorem.
  table of contents: 7.2 The fundamental theorem of calculus and its analog for line integrals7.3 Cap independence; 7.4 Green's and Stokes's theorems; 7.5 Gauss's theorem; 7.6 Proof of the GST; 7.7 The converse of the GST; 7.8 Exercises; 8 de Rham Cohomology; 8.1 Linear and homological algebra constructions; 8.2 Definition and basic properties; 8.3 Computations of cohomology groups; 8.4 Cohomology with compact supports; 8.5 Exercises; Index; A; B; C; D; E; F; G; H; I; L; M; N; O; P; R; S; T; V; W.
  note: by Steve Weintraub.
  note: Includes bibliographical references and index.
  subject:
    topic: Differential forms
  subject:
    topic: Formes différentielles
  subject:
    topic: MATHEMATICS
    topic: Calculus
  subject:
    topic: MATHEMATICS
    topic: Mathematical Analysis
  subject:
    topic: Differential forms
  subject:
    topic: Differentialform
  classification: QA381 .W45 2014
  classification: 515/.37
  related item:
    identifier: (DLC) 2013035820
  identifier: 0123946174
  identifier: 9780123946171
  identifier: 9780123944030
  identifier: 0123944031
  identifier: CL0500000410 Safari Books Online
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: YDXCP
    record creation date: 140314
    record change date: 20260326200328.7
    record identifier: in00005753972
    language of cataloging:
      language term: eng