Analysis with Ultrasmall Numbers
Published on 1. December 2014
316 pages
978-1-4987-0266-9 (ISBN)
Description
Analysis with Ultrasmall Numbers presents an intuitive treatment of mathematics using ultrasmall numbers. With this modern approach to infinitesimals, proofs become simpler and more focused on the combinatorial heart of arguments, unlike traditional treatments that use epsilon-delta methods. Students can fully prove fundamental results, such as the
Reviews / Votes
"This book presents an alternative approach to differential and integral calculus of functions of one variable. ... For readers familiar with the classical methods of mathematical analysis, this book can provide an interesting alternative view."-Zentralblatt MATH 1317
"What the book does exceptionally well is explain and develop the basic notions and machinery slowly, invitingly, methodically, and enjoyably. ... Numerous solved exercises make the book highly efficient in learning the nonstandard technique it advocates but also for learning the elements of calculus ... the book is a well-aimed stab at the heart of the teaching of analysis and presents a very interesting nonstandard approach. Any student intrigued by the subject of nonstandard analysis will find the book to be entertaining and well-written, and to present a coherent approach at a very elementary level."
-MAA Reviews, March 2015
More details
Series
Language
English
Place of publication
Philadelphia, PA
United States
Publishing group
Taylor & Francis Inc
Target group
Professional and scholarly
Researchers interested in non-standard analysis and the theory of infinitesimal numbers; first-year graduate and advanced undergraduate students in analysis or real analysis courses.
Illustrations
21 s/w Abbildungen
21 b/w images
File size
2,42 MB
ISBN-13
978-1-4987-0266-9 (9781498702669)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Karel Hrbacek | Olivier Lessmann | Richard O'Donovan
Analysis with Ultrasmall Numbers
Book
10/2024
1st Edition
Chapman & Hall/CRC
€81.00
Shipment within 10-20 days
Karel Hrbacek | Olivier Lessmann | Richard O'Donovan
Analysis with Ultrasmall Numbers
Book
12/2014
1st Edition
Chapman & Hall/CRC
€161.50
Article not available at the moment
Persons
Karel Hrbacek, Olivier Lessmann, Richard O'Donovan
Content
ELEMENTARY ANALYSIS: Basic Concepts. Continuity and Limits. Differentiability. Elementary Integration. HIGHER ANALYSIS: Basic Concepts Revisited. Derivatives. Sequences and Series. Topology of Real Numbers. Differential Equations. Integration. Appendix. Index.
