- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
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
Contents
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
