© 2008

Analysis by Its History

  • E. Hairer
  • G. Wanner


  • 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 Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-x
  2. E. Hairer, G. Wanner
    Pages 1-79
  3. E. Hairer, G. Wanner
    Pages 80-169
  4. E. Hairer, G. Wanner
    Pages 170-270
  5. E. Hairer, G. Wanner
    Pages 271-350
  6. Back Matter
    Pages 351-379

About this book


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


Isaac Newton calculus derivative differential equation history of mathematics integral integration interpolation

Editors and affiliations

  • E. Hairer
    • 1
  • G. Wanner
    • 1
  1. 1.Department of MathematicsUniversity of GenevaGenevaSwitzerland

Bibliographic information

  • Book Title Analysis by Its History
  • Authors Ernst Hairer
    Gerhard Wanner
  • Series Title Undergraduate Texts in Mathematics
  • DOI
  • Copyright Information Springer Science+Business Media New York 2008
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-0-387-94551-4
  • Softcover ISBN 978-0-387-77031-4
  • eBook ISBN 978-0-387-77036-9
  • Series ISSN 0172-6056
  • Series E-ISSN 2197-5604
  • Edition Number 1
  • Number of Pages X, 379
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Real Functions
    History of Mathematical Sciences
  • Buy this book on publisher's site


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