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Dahan Damedico Amy. The aim of this article is to follow up this theme in his subsequent work during the period, by considering in particular the following aspects: the systematic use of the Fourier transform written with the help of an imaginary variable, the enhanced algebraization of symbolic calculus, the employment of residual calculus.

With the help of these techniques Cauchy arrives at a sixfold integral, a solution to the "Cauchy problem" under consideration. We mention how as early as , in view of applications in optics, Cauchy seeks to reduce this integral; however, to reduce the general integral of equations relating to the vibration of punctiform ether will be the aim of a genuine research program in the s, which I will not examine here.

C'est ce que nous allons examiner ici. Les objectifs en Nous nous limitons d'abord, comme Cauchy, au cas des edp sans second membre. B ei ux-bt une solution de A. Ceci veut dire que pour une direction. Les membres de droite, pour tout y, sont connus. Cauchy obtient la solution sous la forme :. Les coefficients A,, B,, etc.

Dans la plupart des cas, Cauchy prend, comme facteurs auxiliaires de convergence, l'une des expressions suivantes :. Regardons la preuve que donne Cauchy, dans le cas d'une fonction d'une seule variable. La valeur de A est fournie par :. Cauchy choisit. Soient Aq, Ab En fait on verra qu'on a :. Cauchy trouve :. V -1, etc. Il vient :. D'ailleurs, il fait remarquer :. La solution contient n constantes arbitraires.

Par une analogie formelle des calculs, Cauchy montre que la solution est :. D,, D,, Nous voulons. Cauchy A. Savants Etrangers, 1 , dans OC 1 , I, Paris, dans OC 2 , II, OC 2 , XI, Courant-Hilbert, [] Methods of Mathematical Physics, vol. II, new ed. Dahan Dalmedico A. Fourier J. Grattan-Guinness I. Hadamard J. France, 52, Poisson D. I , III , Petrova S. Plucker J. Cauchy [a], p. Courant-Hilbert [], F r F r 28 Cauchy []. Cauchy obtient la solution sous la forme :! V P, 0, 0, Jl dxpdyqdz Notes 1.


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Posts Likes Following Archive. Cours de mathematiques, tome 4 : Equations differentielles, integrales multiples [French] by J. Equations differentielles. Integrales multiples.

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