Standard and Nonstandard Analysis - Fundamental Theory, Techniques and Applications (Hardcover)

Nonstandard analysis is now recognized as a powerful tool in a wide variety of mathematical disciplines, but while there are several books now available in this area, they generally presume some prior knowledge of mathematical analysis. This new text offers an orthodox course in the foundations of elementary analysis and provides a straightforward introduction to nonstandard concepts and techniques. Infinitesimals are introduced in a rigorous context at a comparatively early stage in the discussion of real analysis, and are treated as a natural element in the development of the basic theory of number systems. The approach adopted in this book makes the text accessible not merely to those intending to specialize in mathematics but also to physicists, engineers and students in related disciplines with strong mathematical needs.