Cauchy’s Cours d’analyse: An Annotated Translation

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Springer Science & Business Media, Jan 14, 2010 - Mathematics - 412 pages
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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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Contents

IV
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VI
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VII
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VIII
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IX
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X
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XI
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XXXI
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XXXII
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XXXIII
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XXXIV
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XXXV
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XXXVI
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XXXVII
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XXXVIII
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XLVIII
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XLIX
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L
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LI
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LII
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LIII
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LIV
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LV
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LVI
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About the author (2010)

Baron Augustin Cauchy was one of the great figures of French science in the early nineteenth century. Born in Paris, Cauchy originally studied to become an engineer. Although he began his career as an engineer, illness forced him into mathematics. Cauchy made contributions to a wide variety of subjects in mathematical physics and applied mathematics. His most important work was in pure mathematics. As a mathematician, Cauchy made major contributions to the theory of complex functions. His name is still attached to the Cauchy-Reimann equations, as well as to other fundamental concepts in mathematics, including the Cauchy integral theorem with residues, Cauchy sequences, and the Cauchy-Kovalevskaya existence theorem for the solution of partial differential equations. As a professor at France's famous scientific school, the Ecole Polytechnique, Cauchy taught mathematics to the country's most able future scientists. His interest in presenting fundamental concepts through clear definitions and proofs through detailed and careful arguments is reflected in the textbooks he wrote. In fact, many mathematicians in the nineteenth century first learned their mathematics from the textbooks. Above all, Cauchy was responsible for the famous +g3---+le (delta-epsilon) method for defining many fundamental concepts in mathematics, including limits, continuity, and convergence. As a result, he could establish rigorously basic propositions of calculus. He was also the first to give an existence proof for the solution of a differential equation, as well as for a system of partial differential equations. After the revolution of 1830 in France, Cauchy was forced to live in exile in Italy and Czechoslovakia.

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