Leçons sur les systèmes d'équations aux dérivées partielles

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    PROF. M. JANET has produced a valuable contribution to the analytical theory of partial differential equations. It opens with a clearly written introduction in which are discussed the chief problems arising out of the general theory to be considered. Then follow two chapters on “Calcul inverse de la dérivation”, existence theorems, and the linear partial equation of the second order in one unknown function. These chapters lead logically to the development of the most important part of the subject with which the book is concerned, namely, the reduction of any system of equations to the canonical system of Riquier. The final chapter is devoted to systems in involution, in which another canonical form is considered. This is based upon M. Cartan's development of the Pfaffian system.

    Leçons sur les systèmes d'équations aux dérivées partielles.

    Par Prof. Maurice Janet. (Cahiers scientifiques, Fascicule 4.) Pp. viii + 125. (Paris: Gauthier-Villars et Cie, 1929.) 30 francs.

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