Infinitesimal Methods For Mathematical Analysis

This modern introduction to infinitesimal methods is a translation of the book Metodos Infinitesimais de Analise Matematicaby Jose Sousa Pinto of the University of Aveiro, Portugal and is aimed at final year or graduate level students having a background in calculus. Surveying modern reformulations of the infinitesimal concept with a thoroughly comprehensive exposition of important and influential hyperreal numbers, the book includes previously unpublished material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis. This translation by Roy Hoskins was also greatly assisted by the comments and constructive criticism of Professor Victor Neves, of the University of Aveiro.Pinto, J. Sousa is the author of 'Infinitesimal Methods For Mathematical Analysis', published 2004 under ISBN 9781898563990 and ISBN 1898563993.