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  1. Home
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  3. A Primer of Infinitesimal Analysis
  • Cited by 40
Publisher:
Cambridge University Press
Online publication date:
January 2010
Print publication year:
2008
Online ISBN:
9780511619625
DOI:
https://doi.org/10.1017/CBO9780511619625
Subjects:
Mathematics, Logic, Categories and Sets
Information

Book description

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.

Reviews

'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.'

Source: MAA Reviews

‘John Bell has done a first rate job in presenting an elementary introduction to this fascinating subject ... I recommend it highly.’

J. P. Mayberry Source: British Journal for the Philosophy of Science

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Contents

Contents
References
References
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