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: Undergraduate Analysis
  name:
    name part: Lang, Serge.
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: nyu
    date issued: 1997
    edition: Second edition.
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (xv, 642 pages)
  abstract: This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. Topics discussed include the classical test for convergence of series, Fourier series, polynomial approximation, the Poisson kernel, the construction of harmonic functions on the disc, ordinary differential equation, curve integrals, derivatives in vector spaces, multiple integrals, and others. In this second edition, the author has added a new chapter on locally integrable vector fields, has rewritten many sections and expanded others. There are new sections on heat kernels in the context of Dirac families and on the completion of normed vector spaces. A proof of the fundamental lemma of Lebesgue integration is included, in addition to many interesting exercises.
  table of contents: Review of Calculus: Sets and Mappings. Real Numbers. Limits and Continuous Functions. Differentiation. Elementary Functions. The Elementary Real Integral -- Convergence: Normed Vector Spaces. Limits. Compactness. Series. The Integral in One Variable -- Applications of the Integral: Fourier Series. Improper Integrals. The Fourier Integral -- Calculus in Vector Spaces: Function on n-Space. The Winding Number and Global Potential Functions. Derivatives in Vector Spaces. Inverse Mapping Theorem. Ordinary Differential Equations -- Multiple Integration: Multiple Integrals. Differential Forms -- Appendix -- Index.
  note: by Serge Lang.
  note: Electronic resource.
  subject:
    topic: Mathematics
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: Mathematics
  classification: QA299.6-433
  classification: 515
  related item:
    title info:
      title: Undergraduate texts in mathematics
  identifier: 9781475726985 (electronic bk.)
  identifier: 1475726988 (electronic bk.)
  identifier: 9781441928535
  identifier: 1441928537
  identifier: 1475726988
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: AU@
    record creation date: 130125
    record change date: 20260422200648.4
    record identifier: in00003558254
    language of cataloging:
      language term: eng