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: Resources for the study of real analysis
  name:
    name part: Brabenec, Robert L
    role:
      role term: creator
    role:
      role term: author
  name:
    name part: Mathematical Association of America
  type of resource: text
  genre: bibliography
  genre: exercise books.
  genre: Problems and exercises
  genre: Problems and exercises.
  genre: Problèmes et exercices.
  origin info:
    place:
      place term: dcu
    date issued: 2004
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: print
    extent: xii, 231 pages : illustrations ; 27 cm.
  abstract: "This book is a collection of materials gathered by the author while teaching real analysis over a period of years. It is intended for use as a supplement to a traditional analysis textbook, or to provide material for seminars or independent study in analysis and its historical development. The book includes historical and biographical information, a wide range of problem types, selected readings on a variety of topics, and many references for additional study. Since all these materials are collected into a single book, teachers and students can easily choose items most suitable for their purpose. Teachers may use the book as a supplement to their courses, while students may read much of the book on their own. No other book has been written specifically as a supplement for a real analysis course."--Publisher
  table of contents: Review of Calculus -- Analysis Problems -- Essays.
  table of contents: I. Review of calculus. An outline of a traditional course in calculus -- Calculus review problems -- II. Analysis problems. Basic problems. Properties of even and odd functions -- Use of the cancellation principle -- Finding Maclaurin series representations -- Evaluating ... by Cavalieri sums -- Supplementary problems. The pervasive nature of sequences -- Counterexamples -- Some examples of unusual functions -- Identifying interior, exterior, boundary, and limit points -- Exploring uniform continuity -- Comparing the ratio test, the root test, and Raabe's test -- Various proofs ... -- Finding a value for ... -- Rearrangements of conditionally convergent series -- Finding approximations for [pi]-- A function with derivatives of all orders, but no Maclaurin series -- Evaluating ... by Fermat's method -- Two proofs that ... -- Evaluating ... by Bernoulli's method -- Some interesting sequences of functions -- Comparing uniform continuity and uniform convergence -- Questions for sequences of functions and for series of functions -- Enrichment problems. Generalizing the Fibonacci sequence -- Euler's proof the e is irrational -- Subseries of the harmonic series -- Finding functions whose Maclaurin series is ... -- A pascal-like triangle -- Finding areas without antiderivatives -- Questions from the Euler-Stirling correspondence -- The Gamma function -- Bernoulli numbers -- A look at Fourier series -- Summability of divergent series -- Lebesque measure -- Cantor's middle third set -- III. Essays. History and biography. The time of Archimedes and other giants (pre-1660) -- The time of Newton and Leibniz (1660-1690) -- The time of Euler and the Bernoullis (1690-1790) -- The time of Cauchy, Fourier, and Lagrange (1790-1850) -- The time of Riemann and Weierstrass (1850-1900) -- The time of Lebesgue and Hardy (1900-1940) -- New looks at calculus content. Obtaining the derivative formulas -- Tests for convergence of series -- General topics for analysis. Proof techniques in analy…
  note: by Robert L. Brabenec.
  note: Includes bibliographical references and index.
  subject:
    topic: Mathematical analysis
    genre: Problems, exercises, etc
  subject:
    topic: Functions of real variables
  subject:
    topic: Mathematical analysis
  subject:
    topic: Fonctions de variables réelles
  subject:
    topic: Analyse mathématique
  subject:
    topic: Analyse mathématique
    genre: Problèmes et exercices
  subject:
    topic: Functions of real variables
  subject:
    topic: Mathematical analysis
  classification: QA301 .B73 2004
  classification: 515
  classification: 31.41
  related item:
    title info:
      title: Classroom resource materials
  identifier: 0883857375
  identifier: 9780883857373
  identifier: 2004102964
  identifier: https://www.loc.gov/catdir/toc/fy0601/2004102964.html
  related item:
    location:
      url: https://www.loc.gov/catdir/toc/fy0601/2004102964.html
  location:
    physical location: TAG TAGC
  record info:
    record content source: CUD
    record creation date: 040226
    record change date: 20240808225358.2
    record identifier: in00004817674
    language of cataloging:
      language term: eng