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Neutrices and External Numbers

Neutrices and External Numbers

Autorzy
Wydawnictwo Productivity Press Inc
Data wydania 01/06/2019
Wydanie Pierwsze
Liczba stron 342
Forma publikacji książka w twardej oprawie
Poziom zaawansowania Dla szkół wyższych i kształcenia podyplomowego
Język angielski
ISBN 9781498772679
Kategorie Teoria mnogości, Rachunek matematyczny i analizy matematyczne, Matematyka stosowana
599.00 PLN (z VAT)
$156.36 / €141.06 / £119.06 /
Produkt dostępny
Dostawa 2 dni
Ilość
Do schowka

Opis książki

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 The book Neutrices and External numbers: A Flexible Number System by Bruno Dinis and Imme van den Berg provides a remarkable presentation of the system of external numbers. It is a rigorous and convenient mathematical theory that provides a strong foundation for a complete doctrine of orders of magnitude - the art of neglecting-so present in the scientific approach. This subject is exposed in a pedagogical and comprehensive way by multiplying the points of view and the applications. -Retired Professor Guy Wallet, La Rochelle University, France [. . .] The latest addition to the outstanding CRC Press 'Monographs and Research Notes In Mathematics' series, Neutrices and External Numbers: A Flexible Number System by Bruno Dinis and Imme van den Berg (who is an Associated Professor in Mathematics at the University of Evora, Portugal and whose main area of interest lies in non-standard analysis) is enhanced for academia with an informative five page Foreword, as well as the inclusion of a twelve page Bibliography and a four page Index -- making is a significant and unreservedly recommended addition to professional, college, and university library Advanced Mathematics collections and supplemental

Neutrices and External Numbers

Spis treści

1 Introduction to Elementary Nonstandard Analysis


2 Some models and calculations involving imprecisions.


3 Neutrices and external numbers


4 Advanced properties


5 Sequences. Convergence up to a neutrix


6 Functions of external numbers


7 Integration of functions of external numbers


8 Flexible systems of linear equations


9 Applications in asymptotics


10 Applications in other fields


11 External numbers as a complete arithmetical solid


A Background on Nonstandard Analysis


B Solutions to selected exercises

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