Niels Henrik Abel (1802-29) was one of the most prominent mathematicians in the first half of the nineteenth century. His pioneering work in diverse areas such as algebra, analysis, geometry and mechanics has made the adjective 'abelian' a commonplace in mathematical writing. These collected works, first published in two volumes in 1881 after careful preparation by the mathematicians Ludwig Sylow (1832-1918) and Sophus Lie (1842-99), contain some of the pillars of mathematical history. Volume 1 includes perhaps the most famous of Abel's results, namely his proof of the 'impossibility theorem', which states that the general fifth-degree polynomial is unsolvable by algebraic means. Also included in this volume is Abel's 'Paris memoir', which contains his many fundamental results on transcendental functions - in particular on elliptic integrals, elliptic functions, and what are known today as abelian integrals.
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Höhe: 254 mm
Breite: 178 mm
Dicke: 34 mm
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ISBN-13
978-1-108-05057-9 (9781108050579)
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Schweitzer Klassifikation
Preface; 1. Methode generale pour trouver des fonctions d'une seule quantite variable; 2. Solution de quelques problemes; 3. Memoire sure les equations algebriques; 4. L'integrale finie; 5. Petit contribution a la theorie de quelques fonctions transcendantes; 6. Recherche des fonctions de deux quantites variables; 7. Demonstration de l'impossibilite; 8. Remarque sure le memoire no. 4; 9. Resolution d'un probleme de mecanique; 10. Demonstration d'une expression de laquelle la formule binome est un cas particulier; 11. Sur l'integration de la formule differentielle; 12. Memoire sur une propriete generale; 13. Recherche de la quantite; 14. Recherches sur la serie; 15. Sur quelques integrales definies; 16. Recherches sur les fonctions elliptiqes; 17. Sur les fonctions qui satisfont a l'equation; 18. Note sur un memoire de M. Olivier; 19. Solution d'un probleme general; 20. Addition au memoire precedant; 21. Remarques sur quelques proprietes generales; 22. Sur le nombre des transformations differentes; 23. Theoreme general sur la transformation des fonctions elliptiques; 24. Note sur quelques formules elliptiques; 25. Memoire sur une classe particuliere d'equations; 26. Theoremes sur les fonctions elliptiques; 27. Demonstration d'une propriete generale d'une certaine classe de fonctions transcendantes; 28. Precis d'une theorie des focntions elliptiques. 29. Theoremes et problemes.
