A Primer of Infinistesimal Analysis

2. Auflage 2008
ISBN: 978-0-521-88718-2
Verlag: Cambridge University Press

Buch, Englisch, 140 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 361 g

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.

Autoren/Hrsg.

Bell, John L.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik

Inhaltsverzeichnis

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.

Über Autor(innen)

Bell, John L.
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.