A History of Analysis
About this Title
Hans Niels Jahnke, University of Essen, Essen, Germany, Editor
Publication: History of Mathematics
Publication Year: 2003; Volume 24
ISBNs: 978-0-8218-2623-2 (print); 978-1-4704-3892-0 (online)
MathSciNet review: MR1998242
MSC: Primary 01A05; Secondary 01-06, 26-03, 28-03, 34-03, 46-03, 49-03
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.
General mathematical audience; mathematical historians.
Table of Contents
- Precursors of differentiation and integration
- Newton’s method and Leibniz’s calculus
- Algebraic analysis in the 18th century
- The origins of analytic mechanics in the 18th century
- The foundation of analysis in the 19th century
- Analysis and physics in the nineteenth century: The case of boundary-value problems
- Complex function theory, 1780–1900
- Theory of measure and integration from Riemann to Lebesgue
- The end of the science of quantity: Foundations of analysis, 1860–1910
- Differential equations: A historical overview to circa 1900
- The calculus of variations: A historical survey
- The origins of functional analysis