A Primer of Infinistesimal Analysis

One of the most remarkable recent occurrences in mathematics is the re-founding on a rigorous basis the idea of infinitesimal quantity a notion which played an important role in the early development of the calculus and mathematical analysis. In this new and updated edition basic calculus together with some of its applications to simple physical problems are presented through the use of a straightforward rigorous axiomatically formulated concept of zero-square or nilpotent infinitesimal - that is a quantity so small that its square and all higher powers can be set to zero. The systematic employment of these infinitesimals reduces the differential calculus to simple algebra and at the same time restores to use the infinitesimal methods figuring in traditional applications of the calculus to physical problems - a number of which are discussed in this book. This edition also contains an expanded historical and philosophical introduction.