Imprévus et pièges des cordes vibrantes chez D'Alembert (1755-1783).
Doutes et certitudes sur les équations aux dérivées partielles, les séries et les fonctions

Abstract : This PhD thesis was prepared in the context of a long-term project : the critical and commented edition of D'Alembert's complete works. This scientist is indisputably the pioneer of the partial derivative equations and their application to physical sciences. However, only part of his writings about this subject was really examined by historians of sciences until now. A thorough study of his late memories late allows to modify many appreciations, in particular on the following points: integration and resolution of the equations with or without what we would call "boundary conditions", problems of definition and regularity of the functions, convergence and divergence of the series, development of the functions in power or trigonometrical series... We show here the relevance and the fruitfulness of the results of D'Alembert, but also of hs doubts and the tracks he proposes to enlight them.
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Theses
Mathematics [math]. Université Claude Bernard - Lyon I, 2007. French


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Contributor : Guillaume Jouve <>
Submitted on : Monday, May 4, 2009 - 5:14:02 PM
Last modification on : Tuesday, May 5, 2009 - 8:22:06 AM

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Guillaume Jouve. Imprévus et pièges des cordes vibrantes chez D'Alembert (1755-1783).
Doutes et certitudes sur les équations aux dérivées partielles, les séries et les fonctions. Mathematics [math]. Université Claude Bernard - Lyon I, 2007. French. <tel-00380952>

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