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Look Inside A Primer of Infinitesimal Analysis

A Primer of Infinitesimal Analysis

2nd Edition

$71.95

  • Date Published: May 2008
  • availability: Available
  • format: Hardback
  • isbn: 9780521887182

$ 71.95
Hardback

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About the Authors
  • One of the most remarkable recent occurrences in mathematics is the refounding, on a rigorous basis, of the idea of infinitesimal quantity, a notion which played an important role in the early development of the calculus and mathematical analysis. In this new edition basic calculus, together with some of its applications to simple physical problems, are presented through the use of a straightforward, rigorous, axiomatically formulated concept of 'zero-square', or 'nilpotent' infinitesimal - that is, a quantity so small that its square and all higher powers can be set, literally, to zero. The systematic employment of these infinitesimals reduces the differential calculus to simple algebra and, at the same time, restores to use the “infinitesimal” methods figuring in traditional applications of the calculus to physical problems - a number of which are discussed in this book. This edition also contains an expanded historical and philosophical introduction.

    • Unique treatment of this material at this level
    • First elementary book to employ 'zero-square' infinitesimals in presenting the calculus
    • This new edition fully updated with new material on applications to physics
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    Reviews & endorsements

    'This might turn out to be a boring, shallow book review: I merely LOVED the book...the explanations are so clear, so considerate; the author must have taught the subject many times, since he anticipates virtually every potential question, concern, and misconception in a student's or reader's mind.' MAA Reviews

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    Product details

    • Edition: 2nd Edition
    • Date Published: May 2008
    • format: Hardback
    • isbn: 9780521887182
    • length: 140 pages
    • dimensions: 235 x 156 x 15 mm
    • weight: 0.33kg
    • contains: 54 exercises
    • availability: Available
  • Table of Contents

    Introduction
    1. Basic features of smooth worlds
    2. Basic differential calculus
    3. First applications of the differential calculus
    4. Applications to physics
    5. Multivariable calculus and applications
    6. The definite integral: Higher order infinitesimals
    7. Synthetic geometry
    8. Smooth infinitesimal analysis as an axiomatic system
    Appendix
    Models for smooth infinitesimal analysis.

  • Instructors have used or reviewed this title for the following courses

    • Advanced Mathematical Methods for Engineers
  • Author

    John L. Bell, University of Western Ontario
    John L. Bell is Professor of Philosophy at the University of Western Ontario. He is the author of 7 other books, including Models and Ultraproducts with A. B. Slomson, A Course in Mathematical Logic with M. Machover, Logical Options with D. DeVidi and G. Solomon, Set Theory: Boolean-Valued Models and Independence Proofs, and The Continuous and the Infinitesimal in Mathematics and Philosophy.

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