Abraham Robinson's book, often hailed as his magnum opus, provides a comprehensive exploration of the development and applications of non-standard analysis. As the mathematician who founded this intriguing subject, Robinson sought to address the contradictions posed by infinitesimals within calculus. He first introduced non-standard analysis during a seminar at Princeton in 1960, and the topic continues to spark debate and interest to this day.
This paperback reprint of the 1974 revised edition is essential reading for anyone with an interest in non-standard analysis. Robinson delves into a variety of applications, offering rich detail on topics such as topology, functions of a real variable, functions of a complex variable, and normed linear spaces. Additionally, the book explores complex problems like the boundary layer flow of viscous fluids and provides rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.
For those seeking to understand the profound implications and applications of non-standard analysis, Robinson's work remains an indispensable resource.