Sur la théorie des équations différentielles linéaires
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Sur la théorie des équations différentielles linéaires

Sur la théorie des équations différentielles linéaires


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About the Book

"INTRODUCTION. En 1866, M. Fuchs a publié un Mémoire fondamental1 sur les fonctions d'une va- riable imaginaire définies par une équation différentielle linéaire. M. Tannery a exposé les principes et les résultats de ce travail, en même temps qu'il en a agrandi le cadre par des recherches personnelles2. Depuis, M. Tannery a étudié3 en particulier l'équa- tion qui, dans la théorie des fonctions elliptiques, relie au module la fonction complète de première espèce. A partir de 1868, époque à laquelle parut un second Mémoire de M. Fuchs, l'étude des équations différentielles linéaires, devenue classique en Allemagne, y a donné nais- sance à un grand nombre de travaux. M. Fuchs a persévéré, et deux géomètres émi- nents, MM. Thomé et Fröbenius, ont entrepris des recherches intéressantes et profondes sur ce sujet. J'ai pensé être utile en appelant l'attention sur ces analyses, qui ont leur point de départ dans les découvertes de Cauchy et qui sont la suite naturelle des belles études de M. Puiseux sur les équations algébriques, de MM. Briot et Bouquet sur les équations différentielles du premier ordre. Je me suis donc proposé d'élucider et de compléter le plus possible ces travaux, en prenant pour base les Mémoires de MM. Thomé et Fröbenius. Dans la première Partie, je rappelle les principes fondamentaux de la théorie des équations différentielles linéaires. La deuxième est consacrée à la définition des intégrales régulières et à leur re- cherche, cette recherche étant fondée sur la notion de l'indice caractéristique. Dans la troisième Partie, je définis la fonction caractéristique, la fonction déter- minante, et je ramène la notion de l'indice caractéristique à la considération plus naturelle de la fonction déterminante. Puis on introduit les formes normales, les ex- pressions composées, et l'on établit une proposition capitale concernant la fonction déterminante d'une expression composée de plusieurs formes normales. Enfin, on pose les principes de la réductibilité


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Product Details
  • ISBN-13: 9791041940264
  • Publisher: Bod Third Party Titles
  • Publisher Imprint: Culturea
  • Height: 210 mm
  • No of Pages: 98
  • Spine Width: 6 mm
  • Width: 148 mm
  • ISBN-10: 1041940262
  • Publisher Date: 17 Dec 2022
  • Binding: Paperback
  • Language: French
  • Returnable: N
  • Weight: 186 gr


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