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Look Inside Cours d'analyse de l'École Royale Polytechnique

Cours d'analyse de l'École Royale Polytechnique

Part of Cambridge Library Collection - Mathematics

  • Date Published: July 2009
  • availability: Available
  • format: Paperback
  • isbn: 9781108002080


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About the Authors
  • 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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    Product details

    • Date Published: July 2009
    • format: Paperback
    • isbn: 9781108002080
    • length: 604 pages
    • dimensions: 216 x 140 x 34 mm
    • weight: 0.76kg
    • availability: Available
  • Table of Contents

    Part I. Analyse algébrique:
    1. Des fonctions reélles
    2. Des quantités infiniment petites ou infiniment grandes, et de la continuité des fonctions. Valeurs singulières des fonctions dans quelques cas particuliers
    3. 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
    4. Détermination des fonctions entières, d'après un certain nombre de aleurs particulières supposées connues. Applications
    5 Détermination des fonctions continues d'une seule variable propres à vérifier certaines conditions
    6. Des séries (réelles) convergentes et divergentes. Règles sur la convergence des series. Sommation de quelques séries convergentes
    7. Des expressions imaginaires et de leurs modules
    8. Des variables et des fonctions imaginaires
    9. Des séries imaginaires convergentes et divergentes. Sommation de quelques séries imaginaires convergentes. Notations employées pour représenter quelques fonctions imaginaires auxquelles on se trouve conduit par la sommation de ces mêmes séries
    10. 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 cette espèce par l'algèbre ou la trigonométrie
    11. Décomposition des fractions rationnelles
    12. Des séries récurrentes

  • Author

    Augustin-Louis Cauchy

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