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A History of Analysis
Edited by: Hans Niels Jahnke, University of Essen, Germany
A co-publication of the AMS and the London Mathematical Society.
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History of Mathematics
2003; 422 pp; hardcover
Volume: 24
ISBN-10: 0-8218-2623-9
ISBN-13: 978-0-8218-2623-2
List Price: US$98
Member Price: US$78.40
Order Code: HMATH/24
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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.

Readership

General mathematical audience; mathematical historians.

Reviews

"This book is very good at tying biographies to the development of the mathematics and to the related developments in science ... for the majority of the mathematicians listed here, this [book] is an outstanding starting point ... recommended for academic and research mathematics, physics, and history of science collections."

-- E-STREAMS

"It is a highly readable and informative account of the history of analysis."

-- Zentralblatt MATH

Table of Contents

  • R. Thiele -- Antiquity
  • J. van Maanen -- Precursors of differentiation and integration
  • N. Guicciardini -- Newton's method and Leibniz's calculus
  • H. N. Jahnke -- Algebraic analysis in the 18th century
  • M. Panza -- The origins of analytic mechanics in the 18th century
  • J. Lützen -- The foundation of analysis in the 19th century
  • T. Archibald -- Analysis and physics in the nineteenth century: The case of boundary-value problems
  • U. Bottazzini -- Complex function theory, 1780-1900
  • T. Hochkirchen -- Theory of measure and integration from Riemann to Lebesgue
  • M. Epple -- The end of the science of quantity: Foundations of analysis, 1860-1910
  • T. Archibald -- Differential equations: A historical overview to circa 1900
  • C. Fraser -- The calculus of variations: A historical survey
  • R. Siegmund-Schultze -- The origins of functional analysis
  • Index of names
  • Subject index
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