Overview

Nonstandard Analysis enhances mathematical reasoning by introducing new ways of expression and deduction. Distinguishing between standard and nonstandard mathematical objects, its inventor, the eminent mathematician Abraham Robinson, settled in 1961 the centuries-old problem of how to use infinitesimals correctly in analysis. Having also worked as an engineer, he saw not only that his method greatly simplified mathematically proving and teaching, but also served as a powerful tool in modelling, analyzing and solving problems in the applied sciences, among others by effective rescaling and by infinitesimal discretizations. This book reflects the progress made in the forty years since the appearance of Robinson’s revolutionary book Nonstandard Analysis: in the foundations of mathematics and logic, number theory, statistics and probability, in ordinary, partial and stochastic differential equations and in education. The contributions are clear and essentially self-contained.

Full Product Details

Author:   Imme van den Berg ,  Vitor Neves
Publisher:   Springer Verlag GmbH
Imprint:   Springer Verlag GmbH
Edition:   Softcover reprint of hardcover 1st ed. 2007
Dimensions:   Width: 17.00cm , Height: 2.20cm , Length: 24.20cm
Weight:   0.726kg
ISBN:  

9783211998922

ISBN 10:   3211998926
Pages:   401
Publication Date:   13 October 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

Foundations.- The strength of nonstandard analysis.- The virtue of simplicity.- Analysis of various practices of referring in classical or non standard mathematics.- Stratified analysis?.- ERNA at work.- The Sousa Pinto approach to nonstandard generalised functions.- Neutrices in more dimensions.- Number theory.- Nonstandard methods for additive and combinatorial number theory. A survey.- Nonstandard methods and the Erd?s-Turán conjecture.- Statistics, probability and measures.- Nonstandard likelihood ratio test in exponential families.- A finitary approach for the representation of the infinitesimal generator of a markovian semigroup.- On two recent applications of nonstandard analysis to the theory of financial markets.- Quantum Bernoulli experiments and quantum stochastic processes.- Applications of rich measure spaces formed from nonstandard models.- More on S-measures.- A Radon-Nikodým theorem for a vector-valued reference measure.- Differentiability of Loeb measures.- Differential systems and equations.- The power of Gâteaux differentiability.- Nonstandard Palais-Smale conditions.- Averaging for ordinary differential equations and functional differential equations.- Path-space measure for stochastic differential equation with a coefficient of polynomial growth.- Optimal control for Navier-Stokes equations.- Local-in-time existence of strong solutions of the n-dimensional Burgers equation via discretizations.- Infinitesimals and education.- Calculus with infinitesimals.- Pre-University Analysis.

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions