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Introduction to the theory of infinitesimals

Author: K D Stroyan; W A J Luxemburg
Publisher: New York : Academic Press, ©1976.
Series: Pure and applied mathematics (Academic Press), v. 72.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
Infinitesimal analysis Abraham Robinson's solution to an old problem of Leibniz. In 1961 Robinson showed that a nonstandard model of the formal theory of analysis provides a system of hyperreal numbers and provides rigorous foundations for many of the intuitive correct uses of infinitesimals in mathematics. Robinson showed that the structure that formalizes algebraic and order properties of the real numbers can be  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: K D Stroyan; W A J Luxemburg
ISBN: 0126741506 9780126741506
OCLC Number: 2638728
Description: xiii, 326 pages : illustrations ; 24 cm.
Contents: Part 1. Classical infinitesimals ; Introduction : what are infinitesimals? --
A first look at ultrapowers : a model of rational analysis --
Superstructures and their nonstandard models --
Some basic facts about hyperreal numbers --
Appendix A. Preliminary results on ordered rings and fields --
Foundations of infinitesimal calculus --
Topics in infinitesimal calculus --
Part 2. Infinitesimals in functional analysis ; More tools from model theory --
The general theory of monads and infinitesimals --
Compactifications --
Linear infinitesimals and the locally convex hull.
Series Title: Pure and applied mathematics (Academic Press), v. 72.
Responsibility: K.D. Stroyan in collaboration with W.A.J. Luxemburg.

Abstract:

Infinitesimal analysis Abraham Robinson's solution to an old problem of Leibniz. In 1961 Robinson showed that a nonstandard model of the formal theory of analysis provides a system of hyperreal numbers and provides rigorous foundations for many of the intuitive correct uses of infinitesimals in mathematics. Robinson showed that the structure that formalizes algebraic and order properties of the real numbers can be enlarged to include infinitely small and large numbers. Robinson showed that these nonstandard methods can be successfully applied to other branches of mathematics, notably algebraic number theory and topology.

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