A History of Analysis (History of Mathematics, V. 24) (History of Mathematics, 24)

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 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.--jacket. Antiquity / Rudiger Thiele. -- Precursors Of Differentiation And Integration / Jan Van Maanen. -- Newton's Method And Leibniz's Calculus / Niccolo Guicciardini. -- Algebraic Analysis In The 18th Century / Hans Niels Jahnke. -- The Origins Of Analytic Mechanics In The 18th Century / Marco Panza. -- The Foundation Of Analysis In The 19th Century / Jesper Lutzen. -- Analysis And Physics In The Nineteenth Century: The Case Of Boundary-value Problems / Tom Archibald. -- Complex Function Theory, 1780-1900 / Umberto Bottazzini. -- Theory Of Measure And Integration From Riemann To Lebesgue / Thomas Hochkirchen. -- The End Of The Science Of Quantity: Foundations Of Analysis, 1860-1910 / Moritz Epple. -- Differential Equations: A Historical Overview To Circa 1900 / Tom Archibald. -- The Calculus Of Variations: A Historical Survey / Craig Fraser. -- The Origins Of Functional Analysis / Reinhard Siegmund-schultze. Hans Niels Jahnke, Editor. Includes Bibliographical References And Index. 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. 1.1.1. The subject. Some of the basic problems of analysis were also present in geometrical form in Greek mathematics.