Cauchy's Cours d'analyse: An Annotated Translation / Edition 1

Cauchy's Cours d'analyse: An Annotated Translation / Edition 1

by Robert E. Bradley, C. Edward Sandifer
     
 

ISBN-10: 1441905480

ISBN-13: 9781441905482

Pub. Date: 08/18/2009

Publisher: Springer New York

In 1821, Augustin-Louis Cauchy (1789-1857) published a textbook, the Cours d’analyse, to accompany his course in analysis at the Ecole Polytechnique. It is one of the most influential mathematics books ever written. Not only did Cauchy provide a workable definition of limits and a means to make them the basis of a rigorous theory of calculus, but he also

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Overview

In 1821, Augustin-Louis Cauchy (1789-1857) published a textbook, the Cours d’analyse, to accompany his course in analysis at the Ecole Polytechnique. It is one of the most influential mathematics books ever written. Not only did Cauchy provide a workable definition of limits and a means to make them the basis of a rigorous theory of calculus, but he also revitalized the idea that all mathematics could be set on such rigorous foundations. Today, the quality of a work of mathematics is judged in part on the quality of its rigor, and this standard is largely due to the transformation brought about by Cauchy and the Cours d’analyse.

For this translation, the authors have also added commentary, notes, references, and an index.

Product Details

ISBN-13:
9781441905482
Publisher:
Springer New York
Publication date:
08/18/2009
Series:
Sources and Studies in the History of Mathematics and Physical Sciences Series
Edition description:
2009
Pages:
412
Product dimensions:
6.20(w) x 9.20(h) x 1.20(d)

Table of Contents

Translators’ Introduction.- Cauchy's Introduction.- Preliminaries.- First Part: Algebraic Analysis.- On Real Functions.- On Quantities that are Infinitely Small or Infinitely Large, and on the Continuity of Functions.- On Symmetric Functions and Alternating Functions.- Determination of Integer Functions.- Determination of continuous functions of a single variable that satisfy certain conditions.- On convergent and divergent (real) series.- On imaginary expressions and their moduli.- On imaginary functions and variables.- On convergent and divergent imaginary series.- On real or imaginary roots of algebraic equations for which the first member is a rational and integer of one variable.- Decomposition of rational fractions.- On recursive series.- Notes on Algebraic Analysis.- Bibliography.- Index.

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