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25 Remote Warehouse Mathematics- Calculus

Nonstandard Analysis

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Nonstandard Analysis Cover

 

Synopses & Reviews

Publisher Comments:

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." — J.-M. Lévy-Leblond, European Journal of Physics

Brief 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.

Book News Annotation:

Originally published in 1988 (Wiley), and here reissued with revisions, this concise introduction to nonstandard analysis takes an axiomatic internal set theory approach. It starts with an exposition of the theory, followed by self-contained chapters concerning applications. Specific chapters discuss idealization, standardization and transfer, real numbers and numerical functions, continuity, differentiability, integration, invariant means, approximation, differential equations, perturbation of Green functions, and an invariant subspaces problem. Robert (who also translated the text) teaches at the University of Neuch<^a>tel in Switzerland.
Annotation 2004 Book News, Inc., Portland, OR (booknews.com)

Synopsis:

This introduction to nonstandard analysis is based on the axiomatic internal set theory approach. A clear exposition of theory is followed by applications. Includes exercises, hints, and solutions. 1988 edition.

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 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.

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

Product Details

ISBN:
9780486432793
Author:
Robert, Alain M.
Publisher:
Dover Publications
Author:
Mathematics
Location:
Mineola, N.Y.
Subject:
Calculus
Subject:
Nonstandard mathematical analysis
Subject:
General Mathematics
Subject:
Mathematics-Calculus
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
no. 9
Publication Date:
20110731
Binding:
TRADE PAPER
Language:
English
Illustrations:
14 Figs. 8 Drawings
Pages:
176
Dimensions:
1400x1800

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Science and Mathematics » Mathematics » Analysis General
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Nonstandard Analysis New Trade Paper
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Product details 176 pages Dover Publications - English 9780486432793 Reviews:
"Synopsis" by ,
This introduction to nonstandard analysis is based on the axiomatic internal set theory approach. A clear exposition of theory is followed by applications. Includes exercises, hints, and solutions. 1988 edition.
"Synopsis" by ,
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" by , 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.
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