Synopses & Reviews
This wonderful little book by Alain Robert should bring about a complete change in the learning of NSA. The author has accomplished a rare feat in the educational literature. He has succeeded in writing a book which is simple and brilliant, deep and witty, short and far-ranging. This is mathematics teaching at its best." and#151; J.-M. Land#233;vy-Leblond, E
uropean Journal of PhysicsBrief and readable, this introduction to nonstandard analysis is based on the axiomatic IST (internal set theory) approach. The two-part treatment starts with a clear, rigorous exposition of theory, followed by self-contained chapters on applications. Exercises appear at the conclusion of each chapter, with hints in addition to full solutions. Theoretical topics include idealization, standardization and transfer, real numbers and numerical functions, continuity, differentiability, and integration. Chapters involving applications cover invariant means, approximation of functions, differential equations, perturbation of a Green function, and an invariant subspaces problem.
Synopsis
This short, readable introduction to nonstandard analysis is based on the axiomatic or IST approach. A clear and rigorous exposition of theory is followed by self-contained chapters on applications. Each chapter concludes with exercises, with hints as well as full solutions. Unabridged, with minor corrections by the author, republication of the edition published by John Wiley & Sons, New York, 1988.
Synopsis
This concise text is based on the axiomatic internal set theory approach. Theoretical topics include idealization, standardization, and transfer, real numbers and numerical functions, continuity, differentiability, and integration. Applications cover invariant means, approximation of functions, differential equations, more. Exercises, hints, and solutions. "Mathematics teaching at its best." European Journal of Physics. 1988 edition.
Synopsis
This introduction to nonstandard analysis is based on the axiomaticand#160;internal set theory approach. A clear exposition of theory is followed by applications. Includes exercises,and#160;hints, andand#160;solutions. 1988 edition.
Table of Contents
Preface. Conventions, Notations
Part 1. Introduction
1. Idealization
2. Standardization and Transfer
3. Real Numbers and Numerical Functions
4. Continuity
5. Differentiability
6. Integration
Part 2.
7. Invariant Means
8. Approximation of Functions
9. Differential Equations
10. Perturbation of a Green Function
11. Invariant Subspaces Problem
Indications for Exercises. Solutions of Exercises
Bibliography. Index
Basic Principles of NSA. IST Axioms for NSA