Cauchy's Cours d'analyse : an annotated translation

[translated by] Robert E. Bradley, C. Edward Sandifer

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.

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[目次]

  • On real functions..- On infinitely small and infinitely large quantities, and on the continuity of functions. Singular values of functions in various particular cases..- On symmetric functions and alternating functions. The use of these functions for the solution of equations of the first degree in any number of unknowns. On homogeneous functions..- Determination of integer functions, when a certain number of particular values are known. Applications..- Determination of continuous functions of a single variable that satisfy certain conditions..- On convergent and divergent series. Rules for the convergence of series. The summation of several convergent series..- On imaginary expressions and their moduli..- On imaginary functions and variables..- On convergent and divergent imaginary series. Summation of some convergent imaginary series. Notations used to represent imaginary functions that we find by evaluating the sum of such series..- On real or imaginary roots of algebraic equations for which the left-hand side is a rational and integer function of one variable. The solution of equations of this kind by algebra or trigonometry..- Decomposition of rational fractions..- On recurrent series..

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この本の情報

書名 Cauchy's Cours d'analyse : an annotated translation
著作者等 Cauchy, Augustin Louis, baron
Sandifer C. Edward
Sandifer Charles Edward
Bradley Robert E.
書名別名 Cours d'analyse
シリーズ名 Sources and studies in the history of mathematics and physical sciences
出版元 Springer
刊行年月 c2009
ページ数 xx, 411 p.
大きさ 24 cm
ISBN 9781441905482
NCID BA91474679
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言語 英語
原文言語 フランス語
出版国 アメリカ合衆国
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