Cours d'analyse de l'École Royale Polytechnique

Augustin-Louis Cauchy

doi:10.1017/CBO9780511693328

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Augustin-Louis Cauchy

Publisher:: Cambridge University Press
Online publication date:: August 2010
Print publication year:: 2009
First published in:: 1821
Online ISBN:: 9780511693328
DOI:: https://doi.org/10.1017/CBO9780511693328

Subjects:: Mathematics (general), Mathematics, History of Mathematical Texts
Series:: Cambridge Library Collection - Mathematics

55.99 (GBP)

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In 1821, the French mathematician Augustin-Louis Cauchy published Cours d'Analyse de L'École Royale Polytechnique, a textbook designed to teach his students the basic theorems of calculus in as rigorous a way as possible. Cauchy was a pioneer of mathematical analysis, a branch of mathematics concerned with the idea of a limit, whether of a sequence or of a function. This book consists of 12 chapters that discuss real functions, infinitely small and large quantities, substitution groups, symmetrical functions, unknown variables, imaginary functions, and rational fractions in a recurrent series. It also provides formulas for solving various problems, such as converting the sine and cosine of a multiple polynomial arc and the Lagrange interpolation. Cauchy built on the work of Leibniz and Newton and is generally regarded as one of the greatest mathematicians in history. This is a reissue of one of his most important contributions.

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Cours d'analyse de l'École Royale Polytechnique

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Contents

Frontmatter
pp 1-8

INTRODUCTION
pp i-viii

Contents
pp ix-xiv

ERRATA
pp xv-xvi

PRÉLIMINAIRES DU COURS D'ANALYSE
pp 1-18

PREMIÈRE PARTIE

CHAP. I - Des fonctions réelles
pp 19-25

CHAP. II - Des quantités infiniment petites ou infiniment grandes, et de la continuité des Fonctions. Valeurs singulières des fonctions dans quelques cas particuliers
pp 26-69

CHAP. III - Des Fonctions symétriques et des fonctions alternées. Usage de ces fonctions pour la résolution des équations du premier degré à un nombre quelconque d'inconnues. Des fonctions homogènes
pp 70-84

CHAP. IV - Détermination des fonctions entières, d'après un certain nombre de valeurs particulières supposées connues. Applications
pp 85-102

CHAP. V - Détermination des fonctions continues d'une seule variable propres à vérifier certaines conditions
pp 103-122

CHAP. VI - Des séries (réelles) convergentes et divergentes. Règles sur la convergence des séries. Sommation de quelques séries convergentes
pp 123-172

CHAP. VII - Des expressions imaginaires et de leurs modules
pp 173-239

CHAP. VIII - Des variables et des fonctions imaginaires
pp 240-273

CHAP. IX - Des séries imaginaires convergentcs et divergentes. Sommation de quelques séries imaginaires, convergentes. Notations employées pour représenter quelques fonctions imaginaires auxquelles on se trouve conduit par la sommalion de ces mêmes séries
pp 274-328

CHAP. X - Sur les racines réelles ou imaginaires des équations algébriques dont le premier membre est une fonction rationnelle et entière d'une seule variable. Résolution de quelques équations de celle espéce par l'algèbre ou la trigonomćtrie
pp 329-364

CHAP. XI - Décomposition des fractions rationnelles
pp 365-388

CHAP. XII - Des séries récurrentes
pp 389-402

NOTES SUR L'ANALYSE ALGÉBRIQUE

NOTE I - Sur la théorie des quantités positives et négatives
pp 403-437

NOTE II - Sur les formules qui résultent de l'emploi du signe > ou<, et sur les moyennes entre plusieurs quantités
pp 438-459

NOTE III - Sur la résolution numérique des équations
pp 460-520

NOTE IV - Sur le développeinent de la fonction alternée: (y—x) × (z—x) (z—y) × … × (v—x) (v—y) (v—z) … (v—u)
pp 521-524

NOTE V - Sur la formule de Lagrange relative à l'interpolation
pp 525-529

NOTE VI - Des nombres figurés
pp 530-536

NOTE VII - Des séries doubles
pp 537-547

NOTE VIII - Sur les formules qui servent à convertir les sinus ou cosinus des multiples d'un arc en polynomes dont les differens termes ont pour facteurs les puissances ascendantes du sinus ou cosinus de ce même arc
pp 548-560

NOTE IX - Sur les produils composés d'un nombre infini de facteurs
pp 561-576

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