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Cauchy, original, ingenious and prolific analyst. (Romanian) Zbl 0872.01014

The study is organized in four sections, as follows:
1. ‘Cauchy, father of modern mathematical analysis’ establishes the position held by the great mathematician among other famous names of the time (i.e., the first half of the 19th century): Gauss, Lobachevsky, Bolyai, Möbius, Jacobi, Hamilton, Morgan and many others. Cauchy is first remembered for his contributions to the basic ideas of analysis, the infinitesimal calculus, especially. He also established a precise theory of the elementary functions and introduces a defined integral of some continuous functions.
II. ‘The theory of differential equations and with partial derivative’ presents briefly the new method – created also by Cauchy – of integrating linear differential equations of the \(n\) order, with variable coefficients, which introduces the notion of a complete system of particular integrals of the homogeneous equation.
III. ‘Cauchy’s theory of a complex variable’ is the section discussing the contributions brought by Cauchy, as based on the ideas of Euler; in his turn, his investigations were to be developed further by Riemann and Weierstrass.
IV. ‘Cauchy’s originality and personality’ mentions Cauchy’s teachers, Poisson, Ampère, Hachette and Prony, and follows the years of his formation as a highly original man-of-science, whose concerns were even and even broader.
Reviewer: C.Irimia (Iaşi)

MSC:

01A55 History of mathematics in the 19th century

Biographic References:

Cauchy, A.
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