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: Analysis by Its History
  name:
    name part: Hairer, E.
    role:
      role term: editor.
  name:
    name part: Wanner, G.
    role:
      role term: editor.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2008
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: X, 379 p. online resource.
  abstract: This book presents first-year calculus roughly in the order in which it first was discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers. From the reviews: The aim of this interesting new contribution to the series Readings in Mathematics is an attempt to restore the historical order in the presentation of basic mathematical analysis...such a historical approach can provide a very fruitful and interesting approach to mathematical analysis. - Jean Mawhin, Zentralblatt The authors include a large number of once-traditional subjects which have now vanished from the analysis curriculum, at least in the standard American courses. Thus we find continued fractions, elliptic integrals, the Euler-MacLaurin summation formula, etc., most of which are found only in more compendious works. Many of the exercises are inspired by original papers, with the bibliographic references sometimes given. The work is very well illustrated. The book is definitely an analysis text, rather than a history, but a great deal of reliable historical material is included. For those seeking an alternative to the traditional approach, it seems to me to be of great interest. - Thomas Archibald, Mathematical Reviews The authors...have assembled an impressive array of annotated results, quotations, tables, charts, figures and drawings, many copied from original documents....they write with great enthusiasm and with evident affection for both analysis and history. - John Troutman, American Mathematical Monthly.
  table of contents: to Analysis of the Infinite -- Differential and Integral Calculus -- Foundations of Classical Analysis -- Calculus in Several Variables.
  note: edited by E. Hairer, G. Wanner.
  subject:
    topic: Mathematics
  subject:
    topic: Functions of real variables
  subject:
    topic: History
  subject:
    topic: Mathematics
  subject:
    topic: Real Functions
  subject:
    topic: History of Mathematical Sciences
  classification: QA331.5
  classification: 515.8
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Undergraduate Texts in Mathematics, Readings in Mathematics
  identifier: 9780387770369
  identifier: http://dx.doi.org/10.1007/978-0-387-77036-9
  record info:
    record creation date: 100301
    record change date: 20161125121737.0
    record identifier: 978-0-387-77036-9