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
Rezensionen / Stimmen
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 curriculum lists. It should be noted for students, academia, and non-specialist readers with an interest in the subject that "Neutrices and External Numbers" is also available in a digital book format
-Midwest Book Review
Reihe
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Illustrationen
4 s/w Abbildungen
4 Illustrations, black and white
Maße
Höhe: 234 mm
Breite: 156 mm
Gewicht
ISBN-13
978-1-4987-7267-9 (9781498772679)
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 Klassifikation
Bruno Dinis is a postdoc at the Faculdade de Ciencias, University of Lisbon, whose main area of interest is Mathematical Logic, Proof Theory, Nonstandard Analysis, and Philosophy of Mathematics.
Imme van den Berg is Associated Professor in Mathematics at the University of Evora, Portugal. His main area of interest lies in non-standard analysis. He is the author / co-author of 4 books and over 20 articles in the area of non-standard analysis.
Autor*in
University of Lisbon, Portugal
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
