Readings in Mathematics

Analysis by Its History

Authors: Hairer, Ernst, Wanner, Gerhard

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Hardcover $74.95
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  • ISBN 978-0-387-77031-4
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About this Textbook

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

Reviews

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

Table of contents (4 chapters)

  • Introduction to Analysis of the Infinite

    Hairer, E. (et al.)

    Pages 1-79

  • Differential and Integral Calculus

    Hairer, E. (et al.)

    Pages 80-169

  • Foundations of Classical Analysis

    Hairer, E. (et al.)

    Pages 170-270

  • Calculus in Several Variables

    Hairer, E. (et al.)

    Pages 271-350

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-0-387-77036-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $74.95
price for USA
  • ISBN 978-0-387-94551-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $44.95
price for USA
  • ISBN 978-0-387-77031-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Analysis by Its History
Authors
Series Title
Readings in Mathematics
Copyright
2008
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-387-77036-9
DOI
10.1007/978-0-387-77036-9
Hardcover ISBN
978-0-387-94551-4
Softcover ISBN
978-0-387-77031-4
Edition Number
1
Number of Pages
X, 379
Topics