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Nonstandard asymptotic analysis

Author: Imme van den Berg
Publisher: Berlin ; New York : Springer-Verlag, ©1987.
Series: Lecture notes in mathematics (Springer-Verlag), 1249.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This research monograph considers the subject of asymptotics from a nonstandard view point. It is intended both for classical asymptoticists - they will discover a new approach to problems very familiar to them - and for nonstandard analysts but includes topics of general interest, like the remarkable behaviour of Taylor polynomials of elementary functions. Noting that within nonstandard analysis, "small", "large",  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Berg, Imme van den.
Nonstandard asymptotic analysis.
Berlin ; New York : Springer-Verlag, ©1987
(DLC) 87009435
(OCoLC)15489897
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Imme van den Berg
ISBN: 9783540478102 3540478108
OCLC Number: 298578084
Reproduction Notes: Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2010. MiAaHDL
Description: 1 online resource (ix, 187 pages) : illustrations.
Details: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Contents: Four examples of nonstandard reasoning in asymptotics --
Asymptotic expressions for the remainders associated to expansions of type and, where . Asymptotic expressions for the remainders associated to expansions of type, and : critical regions, uniform behaviour --
External sets. Approximation lemma's --
Shadow expansions --
References --
Index/Lexicon. T.
Series Title: Lecture notes in mathematics (Springer-Verlag), 1249.
Responsibility: Imme van den Berg.

Abstract:

Noting that within nonstandard analysis, "small", "large", and "domain of validity of asymptotic behaviour" have a precise meaning, a nonstandard alternative to classical asymptotics is developed.  Read more...

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