Traces the development of the integral and the differential calculus and related theories since ancient times.

This is the first elementary book to employ the concept of infinitesimals.

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 reprint of the 1974 revised edition is indispensable reading for anyone interested (...) in non-standard analysis. It 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. (shrink)

This paper analyzes Leibniz's notorious 'vinculum substantiale', or 'substantial bond', as it appears in his correspondence with the Jesuit philosopher and theologian, Bartholomew Des Bosses. It is shown that, while Leibniz employs the vinculum to address a problem relating to the unity of corporeal substance, it ultimately violates other key principles in his philosophy.