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Le second ordre
Paris, Editions du Palais royal 1973 495pp., ré-édition de l'édition de 1947, tirage numéroté et limité à 1000 exemplaires: ceci porte le no.779, 22cm., reliure d'éditeur, titre doré au dos, texte et intérieur sont frais, avec ex-libris héraldique, bon état, G115675
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4 book(s) with the same title
Sur les équations différentielles du second ordre et d'ordre supérieur dont l'intégrale générale est uniforme. - [PAINLEVÉ TRANSCENDENTALS]
Berlin, Stockholm, Paris, Beijer, 1902. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 25, 1902. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. pp. 1-86.[Entire volume: (4), 383 pp].
First appearance of Painlevé's important paper in which he introduced some of his transcendents, now know as ""Painlevé transcendents"".Painlevé transcendents are solutions to certain nonlinear second-order ordinary differential equations in the complex plane with the Painlevé property (the only movable singularities are poles), but which are not generally solvable in terms of elementary functions. ""In old problems in which the difficulties seemed insurmountable, Painlevé defined new transcendentals for singular points of differential equations of a higher order than the first. In particular he determined every equation of the second order and first degree whose critical points are fixed. The results of these studies are applicable to the equations of analytical mechanics which admit rational or algebraic first integrals with respect to the velocities. Proving, in the words of Hadamard’s éloge, that ""continuing [the work of] Henri Poincaré was not beyond human capacity,"" Painlevé extended the known results concerning the n-body problem. He also corrected certain accepted results in problems of friction and of the conditions of certain equilibriums when the force function does not pass through a maximum.""Paul Painlevé later became the French prime minister.
Sur les équations différentielles du second ordre et d'ordre supérieur dont l'intégrale générale est uniforme. - [PAINLEVÉ TRANSCENDENTALS]
Berlin, Stockholm, Paris, Beijer, 1902. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 25, 1902. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. pp. 1-86.[Entire volume: (4), 383 pp].
First appearance of Painlevé's important paper in which he introduced some of his transcendents, now know as ""Painlevé transcendents"".Painlevé transcendents are solutions to certain nonlinear second-order ordinary differential equations in the complex plane with the Painlevé property (the only movable singularities are poles), but which are not generally solvable in terms of elementary functions. ""In old problems in which the difficulties seemed insurmountable, Painlevé defined new transcendentals for singular points of differential equations of a higher order than the first. In particular he determined every equation of the second order and first degree whose critical points are fixed. The results of these studies are applicable to the equations of analytical mechanics which admit rational or algebraic first integrals with respect to the velocities. Proving, in the words of Hadamard’s éloge, that ""continuing [the work of] Henri Poincaré was not beyond human capacity,"" Painlevé extended the known results concerning the n-body problem. He also corrected certain accepted results in problems of friction and of the conditions of certain equilibriums when the force function does not pass through a maximum.""Paul Painlevé later became the French prime minister.
Sur les équations differentielles du second ordre à points critiques fixes.
(Paris, Gauthier-Villars), 1906. 4to. No wrappers. In: ""Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences"", Tome 143, No 26.. Pp. (1110-) 1208. (Entire issue offered). Painlevé's paper: pp. 1111-1117. Frayed in inner margins, poor paperquality.
First apperance of the paper in which Pailevé introduced the transcendents which bears his name.""The phenomenon of movable singular points was discovered by Fuchs. The study of movable singular points and of nonlinear second orderr equations with and without such singular points was taken up by many men, notably by Paul Painlevé."" (Morris Kline ""Mathematical Thought from Ancient to Modern Times"", p. 737).
Leçons sur l'Intégration des Equations aux Dérivées Partielles du Second Ordre à Deux Variables Indépendantes.
Paris. Librairie Scientifique J. Hermann. 2 volumes in-8. demi-percaline. Titres dorés au dos. Tome I : S.D. Problème de Cauchy - Caractéristiques - Intégrales Intermédiaires. 226 p. Tome II : 1926. La Méthode de Laplace - Les Systèmes en Involution - La Méthode de M. Darboux - Les Equations de la Première Classe - Transformations des Equations du Second Ordre - Généralisations Diverses. 344 p. Nouveau tirage conforme au précédent. Très bon état du tome II. Le tome I comporte de fortes mouillures dans toute la partie supérieure. N'empêche en rien la lisibilité du texte.
