Infinitesimal methods of mathematical analysis
Author(s)
Bibliographic Information
Infinitesimal methods of mathematical analysis
Horwood, 2004
- Other Title
-
Métodos infinitesimais de análise matemática
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Note
Includes bibliographical references (p. 252-254) and index
Description and Table of Contents
Description
This modern introduction to infinitesimal methods is a translation of the book Metodos Infinitesimais de Analise Matematica by Jose Sousa Pinto of the University of Aveiro, Portugal and is aimed at final year or graduate level students with a background in calculus. Surveying modern reformulations of the infinitesimal concept with a thoroughly comprehensive exposition of important and influential hyperreal numbers, the book includes previously unpublished material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis. This translation by Roy Hoskins was also greatly assisted by the comments and constructive criticism of Professor Victor Neves, of the University of Aveiro.
Table of Contents
- Calculus and infinitesimals
- Standard infinitesimal methods
- Introduction to non-standard analysis
- Applications to elementary real analysis
- Further developments
- Foundations of nonstandard analysis
- Hyperfinite analysis
- Hyperfinite representation of distributions
- Hyperfinite fourier analysis
- Appendix A Evolution of the concept of function
- Appendix B The theorem of L?s
- References.
by "Nielsen BookData"