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Full Description
One of the greatest mathematicians of the nineteenth century, Carl Gustav Jacob Jacobi (1804-51) burst into the limelight with his redevelopment, together with Niels Henrik Abel (1802-29), of the theory of elliptic functions. His pioneering work was characterised by the variety of problems tackled and the power of the tools used to tackle them. His lasting influence on rational mechanics, number theory, partial differential equations, complex variable theory and computation is marked by the number of fundamental concepts that bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol, among others). His collected works, comprising treatises, letters and papers written in German, Latin and French, were published in eight volumes between 1881 and 1891. Edited by fellow German mathematician Karl Weierstrass (1815-97), Volume 4 appeared in 1886.
Contents
1. Ueber die Integration der partiellen Differentialgleichungen erster Ordnung; 2. Ueber die Pfaff'sche Methode, eine gewöhnliche lineare Differentialgleichungen zwischen 2n Variabeln; 3. Bemerkung zu der Abhandlung des Herrn Prof. Scherk; 4. Sur le mouvement d'un point et sur un cas particulier du problème des trois corps; 5. Zur Theorie der Variationsrechnung und der Differentialgleichungen; 6. Ueber die Reduction der Integration der partiellen Differentialgleichungen erster Ordnung; 7. Note sur l'intégration des équations différentielles de la dynamique; 8. Neues Theorem der analytischen Mechanik; 9. Sur un théorème de Poisson; 10. Dilucidationes de aequationum differentialium vulgarium systematis; 11. De integratione aequationis differentialis; 12. De motu puncti singularis; 13. Sur un nouveau principe de la méchanique analytique; 14. Sur l'élimination des noeuds dans le problème des trois corps; 15. Zusatz zu der vorhergehenden Abhandlung; 16. Theoria novi multiplicatoris systemati aequationum differentalium vulgarium applicandi; 17. Sul principio dell'ultimo moltiplicatore e suo uso come nuovo principio generale de meccanica; 18. Zwei Beispiele zur neuen Methode der Dynamik; Nachlass.
