Article ID: CBB000954345

La résolution des équations aux dérivées partielles dans les Opuscules mathématiques de D'Alembert (1761--1783) (2009)

unapi

Guilbaud, Alexandre (Author)
Jouve, Guillaume (Author)


Revue d'Histoire des Mathématiques
Volume: 15
Pages: 59--122


Publication Date: 2009
Edition Details: Translated title: [The Resolution of Partial Differential Equations in the Opuscules mathématiques of D'Alembert (1761--1783).] In French.
Language: French

On the basis of the first part of his works, D'Alembert is nowadays considered as the founder of the theory of partial differential equations. His methods of solving these equations in physico-mathematical contexts which can be found in the nine volumes of his Opuscules mathématiques (1761-1783), however, have hardly been studied by historians. Within the scope of this article, we propose to examine this question for his research on vibrating strings and the flow of fluids in this late corpus. This study will enable us to pin down and analyze his approach and the associated concept of solving differential equations. Given the impact of these questions on related fields of research, this leads us to also reconsider his opinion and the development of his ideas with regard to the controversy on arbitrary functions. At the end of this article, we offer an inventory of partial differential equations in all of D'Alembert's works.

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Authors & Contributors
Crépel, Pierre
Alembert, Jean le Rond d'
Malbos, Philippe
Iohara, Kenji
Vissière, Jean-Louis
Tournès, Dominique
Concepts
Mathematics
Differential equations
Calculus
Encyclopedias (history)
Science
Physics
Time Periods
18th century
19th century
Enlightenment
20th century, early
20th century
Places
France
Germany
Institutions
International Centre of Mathematical Research (CIRM)
Société Royale de Médecine
École Polytechnique, Paris
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