The book describes the conceptual development of analysis from antiquity up to the end of the nineteenth century. Intra-theoretical processes are considered as well as the influence of applied problems and biographical and philosophical backgrounds.

The book has thirteen chapters, each written by a leading specialist in the history of mathematics. The first ten chapters tell the story in its temporal succession (narrative order) whereas the last three chapters give surveys on the history of differential equations, the calculus of variations, and functional analysis.

Special features of the book are a separate chapter on the development of the theory of complex functions in the nineteenth century and two chapters on the influence of physics on analysis. One is about the origins of analytical mechanics and one treats boundary value problems of mathematical physics (especially potential theory) in the nineteenth century.

The authors present the history of analysis as near to the historical sources as is possible from the point of view of readability. The book includes comprehensive bibliographies, providing useful listings of the original literature. Mathematical examples are carefully chosen so that readers with a very modest background in mathematics may follow them.

Readership

General mathematical audience; mathematical historians.