**History of Mathematics**

Volume: 24;
2003;
422 pp;
Hardcover

MSC: Primary 01; 26; 28; 30; 31; 33; 34; 35; 40; 45; 49;

Print ISBN: 978-0-8218-2623-2

Product Code: HMATH/24

List Price: $103.00

Individual Member Price: $82.40

**Electronic ISBN: 978-1-4704-3892-0
Product Code: HMATH/24.E**

List Price: $103.00

Individual Member Price: $82.40

#### Supplemental Materials

# A History of Analysis

Share this page *Edited by *
*Hans Niels Jahnke*

A co-publication of the AMS and the London Mathematical Society

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.

#### Table of Contents

# Table of Contents

## A History of Analysis

- Cover Cover11
- Title page i2
- Contents iii4
- Introduction vii8
- Antiquity 112
- Precursors of differentiation and integration 4152
- Newton’s method and Leibniz’s calculus 7384
- Algebraic analysis in the 18th century 105116
- The origins of analytic mechanics in the 18th century 137148
- The foundation of analysis in the 19th century 155166
- Analysis and physics in the nineteenth century: The case of boundary-value problems 197208
- Complex function theory, 1780–1900 213224
- Theory of measure and integration from Riemann to Lebesgue 261272
- The end of the science of quantity: Foundations of analysis, 1860–1910 291302
- Differential equations: A historical overview to circa 1900 325336
- The calculus of variations: A historical survey 355366
- The origins of functional analysis 385396
- Index of names 409420
- Subject index 415426
- Back Cover Back Cover1434

#### 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