résumé leçons données école royale von cauchy augustin louis (8 Ergebnisse)

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Taschenbuch. Zustand: Neu. Neuware.

Taschenbuch. Zustand: Neu. Résumé Des Leçons Données À l'École Royale Polytechnique Sur Le Calcul Infinitésimal Tome 1 | Augustin-Louis Cauchy | Taschenbuch | Kartoniert / Broschiert | Französisch | 2016 | Hachette Livre - BNF | EAN 9782019556754 | Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, 36244 Bad Hersfeld, gpsr[at]libri[dot]de | Anbieter: preigu.

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Taschenbuch. Zustand: Neu. Résumé des leçons données à l'École royale polytechnique sur le calcul infinitésimal | Tome 1 | Augustin Louis Cauchy | Taschenbuch | Französisch | 2025 | Antigonos Verlag | EAN 9783388793030 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu.

First edition. PROVIDED RIGOROUS FOUNDATIONS FOR THE CALCULUS. First edition of the rarest of Cauchy's three great textbooks, which placed "the fundamental principles of the calculus on a satisfactory foundation" (Smith, History of Mathematics II, p. 700). The Résumé, often referred to as the Calcul infinitésimal, is divided into 40 lectures, the first twenty on differential calculus, the remainder on integral calculus, each lecture being precisely four pages in length (so that each lecture could be distributed to the students). It may be regarded as the second part of Cauchy's famous Cours d'analyse (1821) (see below); it gives the first rigorous treatment of calculus proper (differentiation and integration), while the Cours had covered the necessary background concepts (limits, continuity, and convergence). "Within this single text [the Résumé], Cauchy succinctly lays out and rigorously develops all of the topicsone encounters in an introductory study of the calculus, from his classic definition of the limit tohis detailed analysis of the convergence properties of infinite series. In between, the reader willfind a full treatment of differential and integral calculus, including the main theorems of calculusand detailed methods of differentiating and integrating a wide variety of functions. Real, singlevariable calculus is the main focus of the text, but Cauchy spends ample time exploring theextension of his rigorous development to include functions of multiple variables as well ascomplex functions" (Cates). "Cauchy's work set a new standard of mathematical rigor in Europe for the remainder of the 19th century and would finally, after nearly 150 years of attempts, place the calculus on firmly defendable ground (ibid., p. viii). This copy is complete with the important 'Addition' (pp. 161-172), which treats Cauchy's newly discovered mean value theorem and its applications (this is not mentioned in the Table de Matières and is lacking in many copies, including that in the BNF). "Although it is rather less famous than the Cours, the Résumé may have had a more direct influence on the establishment of mathematical analysis, since of course the calculus was the central part of the new discipline founded on limits" (Grattan-Guinness, Convolutions, p. 747). "Cauchy rivaled Euler in mathematical productivity, contributing some 800 books and articles on almost all branches of the subject. Among his greatest contributions are the rigorous methods which he introduced into the calculus in his three great treatises: the Cours d'analyse de l'École Polytechnique (1821), Résumé des leçons sur le calcul infinitesimal (1823), and Leçons sur le calcul differential (1829). Through these works Cauchy did more than anyone else to impress upon the subject the character which it bears at the present time" (Boyer, p. 271). Cauchy's Résumé is a very rare book on the market no copies are listed on ABPC/RBH. The original development of the calculus by Leibniz and Newton had relied on intuitive geometric arguments. Although the majority of scientists and mathematicians accepted the truth of the calculus because of its impressive success in describing and predicting the workings of the natural world, especially in astronomy and mechanics, some, notably Bishop George Berkeley and Michel Rolle, were skeptical about the soundness of its foundations. Their criticisms were addressed by, among others, Colin Maclaurin and Jean le Rond d'Alembert. The next major development came in 1797, when Joseph-Louis Lagrange published his Théorie des fonctions analytiques, based on his lectures at the École Polytechnique. Lagrange used power series expansions to define derivatives, but his approach left open the question as to whether all functions could be expressed as power series. In 1815, just two years after Lagrange died, Cauchy joined the faculty at the École Polytechnique as professor of analysis and started to teach the same course that Lagrange had taught. He inherited Lagrange's commitment to establish proper foundations for the calculus, but he followed Maclaurin and d'Alembert rather than Lagrange and sought those foundations in the formality of limits. A few years later he published his lecture notes as the Cours d'analyse (1821). As its subsidiary title 'Première Partie: Analyse algébrique' suggests, Cauchy intended to write a second part; this appeared two years later as the present work. In the Foreword, Cauchy outlines the philosophy of this work. "This work, undertaken on the request of the Board of Instruction of the Royal Polytechnic School, offers a summary of the lectures that I gave to this school on the infinitesimal calculus. It will be composed of two volumes [sic, see below] corresponding to the two years which form the duration of the course. I publish the first volume today di- vided into forty lectures, the first twenty of which comprise the differential calculus, and the last twenty a part of the integral calculus. The methods that I follow differ in several respects from those which are found expressed in the works of similar type. My main goal has been to reconcile the rigor, which I have made a law in my Analysis Course [i.e., the Cours d'analyse], with the simplicity which results from the direct consideration of infinitely small quantities. For this reason, I thought obliged to reject the expansion of functions by infinite series, whenever the series obtained are not convergent; and I saw myself forced to return the formula of Taylor to the integral calculus, and this formula can only be admitted as general so long as the series that it contains is found reduced to a finite number of terms and supplemented by a definite integral. I am aware that the illustrious author of the Analytical Mechanics [i.e., Lagrange] has taken the formula in question for the basis of his theory of derived functions. But, despite all the respect that such a grand authority commands, the majority of mathematicians are now in accordance.