A Primer of Infinitesimal Analysis - Rilegato

Bell, John L.

Rilegato

ISBN 10: 0521624010 ISBN 13: 9780521624015

Casa editrice: Cambridge University Press, 1998

Riassunto

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 book, 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. As we show, 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. The book also contains a historical and philosophical introduction, a chapter describing the logical features of the infinitesimal framework, and an appendix sketching the developments in the mathematical discipline of category theory that have made the refounding of infinitesimals possible.

Su questo libro

Recensione:

'The book will be of interest to philosophically orientated mathematicians and logicians.' European Mathematical Society

Descrizione del libro:

This book provides an approach to the calculus and its applications to physical problems using a concept of the infinitesimal - that is, of a quantity so small that, while not necessarily zero, it is nevertheless smaller than any finite quantity. This approach enables the calculus to be presented in a particularly straightforward way, avoiding the usual complication associated with the subject. This is the first elementary book to employ the so-called 'zero-square' infinitesimals, and so at the moment it really has no direct competition.

Su questa edizione

• Editore: Cambridge University Press
• Data di pubblicazione: 1998
• ISBN 10: 0521624010
• ISBN 13: 9780521624015
• Rilegatura: Copertina rigida
• Numero di pagine: 136