"This introduction to infinitesimal methods is aimed at undergraduate and graduate level students who have a general background in analysis. It surveys recent reformulations of the infinitesimal concept and gives a comprehensive account of the hyperreal number system and of nonstandard analysis. Applications of nonstandard analysis to calculus, topology and elementary real variable theory illustrate the power and versatility of infinitesimal methods. The presentation of nonstandard treatments of advanced material, in particular of measure theory, integration and generalised functions, is strengthened by an introduction to hyperfinite analysis.The most important material in the book is a hyperfinite theory of Schwartz distributions with applications to generalised Fourier transforms and harmonic analysis, and is not available in any other text on nonstandard methods." — BOOK JACKET.  Read more...
1. Calculus and the infinitesimals —
2. "Standard" infinitesimal methods —
3. Introduction to nonstandard analysis —
4. Applications to elementary real analysis —
5. Further developments —
6. Foundations of nonstandard analysis —
7. Hyperfinite analysis —
8. Hyperfinite representation of distributions —
9. Hyperfinite Fourier analysis —
App. A. Evolution of the concept of function —
App. B. The theorem of Los.