UID:
almahu_9949383511102882
Format:
1 online resource.
ISBN:
9780429155390
,
0429155395
,
9781000012200
,
1000012204
,
9780415016131
,
0415016134
,
9781000005387
,
1000005380
,
9780429291456
,
0429291450
Series Statement:
Monographs and research notes in mathematics
Content:
Neutrices and External Numbers: A Flexible Number System introduces a new model of orders of magnitude and of error analysis, with particular emphasis on behaviour under algebraic operations. The model is formulated in terms of scalar neutrices and external numbers, in the form of an extension of the nonstandard set of real numbers. Many illustrative examples are given. The book starts with detailed presentation of the algebraic structure of external numbers, then deals with the generalized Dedekind completeness property, applications in analysis, domains of validity of approximations of solutions of differential equations, particularly singular perturbations. Finally, it describes the family of algebraic laws characterizing the practice of calculations with external numbers. Features Presents scalar neutrices and external numbers, a mathematical model of order of magnitude within the real number system. Outlines complete algebraic rules for the neutrices and external numbers Conducts operational analysis of convergence and integration of functions known up to orders of magnitude Formalises a calculus of error propagation, covariant with algebraic operations Presents mathematical models of phenomena incorporating their necessary imprecisions, in particular related to the Sorites paradox
Note:
Introduction to elementary nonstandard analysis -- Some models and calculations involving imprecisions -- Neutrices and external numbers -- Advanced properties -- Sequences. Convergence up to a neutrix -- Functions of external numbers -- Integration of functions of external numbers -- Flexible systems of linear equations -- Applications in asymptotics -- Applications in other fields -- External numbers as a complete arithmetical solid
Additional Edition:
Print version: Neutrices and external numbers Boca Raton, Florida : CRC Press, [2019] ISBN 9781498772679 (hardback : alk. paper)
Language:
English
Keywords:
Electronic books.
;
Electronic books.
DOI:
10.1201/9780429291456
URL:
https://www.taylorfrancis.com/books/9780429291456
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