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  • Textbook
  • © 2008

Analysis by Its History

Editors:

  1. E. Hairer

    1. Department of Mathematics, University of Geneva, Geneva, Switzerland

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  2. G. Wanner

    1. Department of Mathematics, University of Geneva, Geneva, Switzerland

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    You can also search for this editor in PubMed   Google Scholar

  • Aims at presenting stimulating and enjoyable coverage of the topics
  • Presents topics in the historical order it was developed in, showing how the ideas inspired further development of each topic
  • Many quotations are included to give the flavor of the history
  • The authors have published other successful titles with Springer

Part of the book series: Undergraduate Texts in Mathematics (UTM)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-x
    PDF

  2. Introduction to Analysis of the Infinite

    • E. Hairer, G. Wanner
    Pages 1-79

  3. Differential and Integral Calculus

    • E. Hairer, G. Wanner
    Pages 80-169

  4. Foundations of Classical Analysis

    • E. Hairer, G. Wanner
    Pages 170-270

  5. Calculus in Several Variables

    • E. Hairer, G. Wanner
    Pages 271-350

  6. Back Matter

    Pages 351-379
    PDF
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About this book

. . . that departed from the traditional dry-as-dust mathematics textbook. (M. Kline, from the Preface to the paperback edition of Kline 1972) Also for this reason, I have taken the trouble to make a great number of drawings. (Brieskom & Knorrer, Plane algebraic curves, p. ii) . . . I should like to bring up again for emphasis . . . points, in which my exposition differs especially from the customary presentation in the text­ books: 1. Illustration of abstract considerations by means of figures. 2. Emphasis upon its relation to neighboring fields, such as calculus of dif­ ferences and interpolation . . . 3. Emphasis upon historical growth. It seems to me extremely important that precisely the prospective teacher should take account of all of these. (F. Klein 1908, Eng\. ed. p. 236) Traditionally, a rigorous first course in Analysis progresses (more or less) in the following order: limits, sets, '* continuous '* derivatives '* integration. mappings functions On the other hand, the historical development of these subjects occurred in reverse order: Archimedes Cantor 1875 Cauchy 1821 Newton 1665 . ;::: Kepler 1615 Dedekind . ;::: Weierstrass . ;::: Leibniz 1675 Fermat 1638 In this book, with the four chapters Chapter I. Introduction to Analysis of the Infinite Chapter II. Differential and Integral Calculus Chapter III. Foundations of Classical Analysis Chapter IV. Calculus in Several Variables, we attempt to restore the historical order, and begin in Chapter I with Cardano, Descartes, Newton, and Euler's famous Introductio.
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Keywords

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Reviews

"...well done, attractively designed...And above all, it proposes an interesting approach to teaching analysis." Internationale Mathematische Nachrichten
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Editors and Affiliations

  • Department of Mathematics, University of Geneva, Geneva, Switzerland

    E. Hairer, G. Wanner

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Bibliographic Information

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Buy it now

eBook USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 44.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 74.95
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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