Analysis with Ultrasmall NumbersKarel Hrbacek, Olivier Lessmann, Richard O'Donovan.

By:

Hrbacek, Karel, 1944- [Author]

Contributor(s):

Material type: Text

text

Media type:

computer

Carrier type:

online resource

ISBN:

9781498702669

Subject(s):

Genre/Form:

Electronic Books.

LOC classification:

QA303 .A535 2015

Online resources:

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Available additional physical forms:

Contents:

Subject: 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 Extreme Value Theorem, from the axioms immediately, without needing to master notions of supremum or compactness. The book is suitable for a calculus course at the undergraduate or high school level or for self-study with an emphasis on nonstandard.

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Holdings
Item type	Current library	Collection	Call number	URL	Status	Date due	Barcode
Online Book (LOGIN USING YOUR MY CIU LOGIN AND PASSWORD)	G. Allen Fleece Library ONLINE	Non-fiction	QA303.2 (Browse shelf(Opens below))	Link to resource	Available		ocn894169680

"A Chapman & Hall book."

Includes bibliographies and index.

Front Cover; Contents; Preface; Preface for Students; Acknowledgments; Authors; Part I: Elementary Analysis; Chapter 1: Basic Concepts; Chapter 2: Continuity and Limits; Chapter 3: Differentiability; Chapter 4: Integration of Continuous Functions; Part II: Higher Analysis; Chapter 5: Basic Concepts Revisited; Chapter 6: L'Hôpital's Rule and Higher Order Derivatives; Chapter 7: Sequences and Series; Chapter 8: First Order Differential Equations; Chapter 9: Integration; Chapter 10: Topology of Real Numbers; Answers to Exercises; Appendix: Foundations and Relative Set Theory; Bibliography.

Back Cover.

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 Extreme Value Theorem, from the axioms immediately, without needing to master notions of supremum or compactness. The book is suitable for a calculus course at the undergraduate or high school level or for self-study with an emphasis on nonstandard.

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