Analysis as an independent subject was created as part of the scientific revolution in the seventeenth century. Kepler, Galileo, Descartes, Fermat, Huygens, Newton, and Leibniz, to name but a few, contributed to its genesis. Since the end of the seventeenth century, the historical progress of mathematical analysis has displayed unique vitality and momentum. No other mathematical field has so profoundly influenced the development of modern scientific thinking. Describing this multidimensional historical development requires an in-depth discussion which includes a reconstruction of general trends and an examination of the specific problems.This volume is designed as a collective work of authors who are proven experts in the history of mathematics. It clarifies the conceptual change that analysis underwent during its development while elucidating the influence of specific applications and describing the relevance of biographical and philosophical backgrounds. The first ten chapters of the book outline chronological development and the last three chapters survey the history of differential equations, the calculus of variations, and functional analysis. Special features 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 the development of boundary-value problems of mathematical physics (especially potential theory) in the nineteenth century. The book presents an accurate and very readable account of the history of analysis. Each chapter provides a comprehensive bibliography. Mathematical examples have been carefully chosen so that readers with a modest background in mathematics can follow them. It is suitable for mathematical historians and a general mathematical audience.
Antiquity by R. Thiele Precursors of differentiation and integration by J. van Maanen Newton's method and Leibniz's calculus by N. Guicciardini Algebraic analysis in the 18th century by H. N. Jahnke The origins of analytic mechanics in the 18th century by M. Panza The foundation of analysis in the 19th century by J. Lutzen Analysis and physics in the nineteenth century: The case of boundary-value problems by T. Archibald Complex function theory, 1780-1900 by U. Bottazzini Theory of measure and integration from Riemann to Lebesgue by T. Hochkirchen The end of the science of quantity: Foundations of analysis, 1860-1910 by M. Epple Differential equations: A historical overview to circa 1900 by T. Archibald The calculus of variations: A historical survey by C. Fraser The origins of functional analysis by R. Siegmund-Schultze Index of names Subject index.