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: Introduction to Calculus and Classical Analysis
  name:
    name part: Hijab, Omar.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2016
    edition: 4th ed. 2016.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 427 p. 69 illus., 1 illus. in color. online resource.
  abstract: This completely self-contained text is intended either for a course in honors calculus or for an introduction to analysis. Beginning with the real number axioms, and involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate math majors. This fourth edition includes an additional chapter on the fundamental theorems in their full Lebesgue generality, based on the Sunrise Lemma. Key features of this text include: • Applications from several parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta functions, transcendental numbers, the Bessel and gamma functions, and many more; • A heavy emphasis on computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero; • Traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals; • A self-contained treatment of the fundamental theorems of calculus in the general case using the Sunrise Lemma; • The integral is defined as the area under the graph, while the area is defined for every subset of the plane; • 450 problems with all the solutions presented at the back of the text. Reviews: "Chapter 5 is…an astonishing tour de force…" —Steven G. Krantz, American Math. Monthly "For a treatment…[of infinite products and Bernoulli series] that is very close to Euler’s and even more elementary…" —V. S. Varadarajan, Bulletin AMS "This is a very intriguing, decidedly unusual, and very satisfying treatment of calculus and introductory analysis. It's full of quirky little approaches to standard topics that make one wonder over and over again, 'Why is it never done like this?'" —John Allen Paulos, Author of Innumeracy and A Mathematician Reads the Newspaper.
  table of contents: Preface -- A Note to the Reader -- 1. The Set of Real Numbers -- 2. Continuity -- 3. Differentiation.-4. Integration -- 5. Applications -- 6. Generalizations -- A. Solutions -- References -- Index.
  note: by Omar Hijab.
  subject:
    topic: Mathematics
  subject:
    topic: Approximation theory
  subject:
    topic: Sequences (Mathematics)
  subject:
    topic: Special functions
  subject:
    topic: Combinatorics
  subject:
    topic: Mathematics
  subject:
    topic: Approximations and Expansions
  subject:
    topic: Sequences, Series, Summability
  subject:
    topic: Special Functions
  subject:
    topic: Combinatorics
  classification: QA401-425
  classification: 511.4
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Undergraduate Texts in Mathematics
  identifier: 9783319284002
  identifier: http://dx.doi.org/10.1007/978-3-319-28400-2
  record info:
    record creation date: 160209
    record change date: 20160218152138.0
    record identifier: 978-3-319-28400-2