Robinson A. Non-standard Analysis

Revised ed. — Amsterdam: North-Holland Publishing Company, 1974. — 309 p. — (Studies in Logic & Foundations of Mathematics). — ISBN: 072042237X.Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.General Introduction.
Tools from Logic.
Differential and Integral Calculus.
General Topology.
Functions of a Real Variable.
Functions of a Complex Variable.
Linear Spaces.
Topological Groups and Lie Groups.
Selected Topics.
Concerning the History of the Calculus.Index of Authors.
Subject Index.