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: Foundations of real and abstract analysis
  name:
    name part: Bridges, D. S. (Douglas S.)
    name part: 1945-
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: nyu
    date issued: 1998
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (xiv, 322 pages)
  abstract: The core chapters of this volume provide a complete course on metric, normed, and Hilbert spaces, and include many results and exercises seldom found in texts on analysis at this level. The author covers an unusually wide range of material in a clear and concise format including elementary real analysis, Lebesgue integration on R, and an introduction to functional analysis. This makes a versatile text also suited for courses on real analysis, metric spaces, abstract analysis, and modern analysis. The book begins with a comprehensive chapter providing a fast-paced course on real analysis, and is followed by an introduction to the Lebesgue integral. This provides a reference for later chapters as well as an introduction for students with only the typical sequence of undergraduate calculus courses as prerequisites. Other features include a chapter introducing functional analysis, the Hahn-Banach theorem and duality, separation theorems, the Baire Category Theorem, the Open Mapping Theorem and their consequences, and unusual applications such as weak solutions of the Dirichlet Problem and Pareto optimality in Mathematical Economics. Of special interest is the unique collection of nearly 750 exercises, many with guidelines for their solutions. The exercises include applications and extensions of the main propositions and theorems, results that fill in gaps in proofs or that prepare for proofs later in the book, pointers to new branches of the subject, and difficult challenges for the very best students.
  table of contents: Cover -- Preface -- Contents -- Introduction -- 1. Analysis on the Real Line -- 2. Differentition and the Lebesgue Integral -- 3. Analysis in Metric Spaces -- 4. Analysis in Normed Linear Spaces -- 5. Hilbert Spaces -- 6. An Introduction to Functional Analysis -- Appendix A -- Appendix B -- Appendix C -- References.
  note: Douglas S. Bridges.
  note: Electronic resource.
  note: Includes bibliographical references (pages 311-315) and index.
  subject:
    topic: Mathematical analysis
  subject:
    topic: Mathematics
  subject:
    topic: Analyse mathematique
  subject:
    topic: MATHEMATICS
    topic: Calculus
  subject:
    topic: MATHEMATICS
    topic: Mathematical Analysis
  subject:
    topic: Mathematical analysis
  classification: QA300 .B69 1998eb
  classification: 515
  related item:
    title info:
      title: Foundations of real and abstract analysis
    name:
      name part: Bridges, D.S. (Douglas S.), 1945-
    origin info:
      publisher: New York : Springer, ©1998
    identifier: (DLC) 97010649
  related item:
    title info:
      title: Graduate texts in mathematics ; 174
  identifier: 0387226206 (electronic bk.)
  identifier: 9780387226200 (electronic bk.)
  identifier: 0585478198 (electronic bk.)
  identifier: 9780585478197 (electronic bk.)
  identifier: 9780387982397
  identifier: 0387982396
  identifier: 9781461459613
  identifier: 1461459613
  identifier: 9781461459620
  identifier: 1461459621
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: MERUC
    record creation date: 970325
    record change date: 20260420211646.7
    record identifier: in00003513471
    language of cataloging:
      language term: eng