Non-Standard Analysis

Nonstandard analysis represents a fundamental change of perspective in mathematics (and sciences), comparable to the introduction of Cantor's set theory in the nineteenth century. This book is a short, readable introduction to the subject, based on the axiomatic or IST approach. The first part gives a clear, rigorous exposition of the theory; the second part consists of a number of self-contained chapters dealing with applications. As an aid to self-study, the author has included exercises at the end of each chapter, with hints as well as full solutions. This book will be invaluable for students, teachers and researchers wishing to learn about nonstandard analysis, either for its applications to other branches of mathematics and science, or for its own sake. Infinitesimals have been hotly debated since the invention of calculus 300 years ago. This accessible treatment of nonstandard analysis (NSA) presents an elementary, yet rigorous account of the theory of infinitesimals and derives some known mathematical results in a nonclassical way. Provides recent solutions to mathematical questions which remained unsolved until the advent of NSA. Treatment is self-contained and includes exercises with detailed solutions. ``This wonderful little book...is simple and brilliant, deep and witty, short and far-ranging...''(--J.-M. Ley-Leblond, European Journal of Physics) Idealization -- Standardization And Transfer -- Real Numbers And Numerical Functions -- Continuity -- Differentiability -- Integration -- Invariant Means -- Approximation Of Functions -- Differential Equations -- Perturbation Of A Green Function -- Invariant Subspaces Problem. Alain Robert ; Translated And Adapted By The Author. Translation Of: L'analyse Non-standard. A Wiley-interscience Publication. Includes Index. Bibliography: P. [153]-154.