Edouard Goursat

Édouard Jean-Baptiste Goursat (born May 21, 1858 in Lanzac , Département Lot , France , † November 25, 1936 in Paris , France) was a French mathematician who is known as the author of a classical analysis textbook.

This star surface examined by Goursat is described with the following formula:
${\displaystyle x^{4}+y^{4}+z^{4}+{\frac {1}{4}}(x^{2}+y^{2}+z^{2})^{2}+{\frac {1}{2}}(x^{2}+y^{2}+z^{2})=1}$

Goursat attended the Collège de Brive-la-Gaillarde and began studying at the École normal supérieure (ENS) in 1876 . There he was influenced in particular by Charles Hermite and Jean Darboux and met Charles Émile Picard , who studied with him and with whom he remained lifelong friends. Picard later persuaded him to embark on a college career. In 1879 he began teaching at the University of Paris and in 1881 received his doctorate for his thesis "Sur l'équation différentialle linéaire qui admet pour intégrale la série hypergéometrique". Goursat then taught in Toulouse until 1885 and then went back to his original university, the ENS. Since his time in Toulouse he has produced numerous publications in various areas of analysis . His famous Cours d´analyse mathématique , which appeared in three volumes from 1902 to 1913 and for which he is best known, arose from his lectures at the ENS . In 1919 Goursat was accepted into the Académie des sciences after he had been elected as a foreign member of the Accademia Nazionale dei Lincei in Rome in 1918.

The Goursat lemma was named after him. In 1895 he was president of the Société Mathématique de France .

Fonts

• Cours d'analysis mathématique, 3 volumes, Paris, Gauthier-Villars, the first two volumes appeared in 1902 and 1905, the second edition with three volumes appeared from 1910 to 1913, 7th edition in 1949 (Volume 1: Dérivées et différentielles. Intégrales définies. Développement en séries. Applications géométriques. Volume 2: Théorie des fonctions analytiques. Equations différentielles. Equations aux dérivées partielles. Éléments du calcul variations. Volume 3: Intégrales infiniment voisines, Équations aux dérivées partielles du second intégrales)
  • English translation by Earle Raymond Hedrick: A course in mathematical analysis, Boston, Ginn and Company 1904–1917 and Dover, 1959, 2005, 3 volumes (Volume 1: Derivates and Differentials: Definite integrals. Expansion in series. Applications to geometry. Volume 2–1: Functions of a complex variable, Volume 2–2: Differential equations, Volume 3–1: Variations of solution: partial differential equations of the second order, Volume 3–2: Integral equations: calculus of variations), O´ Connor and Robertson (McTutor archive) on the Cours d´analysis of Goursat with content
• Lecons sur l'intégration des équations aux derivées partielles du premier ordre, 2nd edition, Paris, Hermann 1921
• Lecons on the problem of Pfaff, Paris, Hermann 1922
• with Paul Appell : Théorie des fonctions algébriques et de leurs intégrales. Étude des fonctions analytiques sur une surface de Riemann, Paris, Gauthier-Villars 1895
• The problem of Bäcklund, Paris, Gauthier-Villars 1925
• Lecons sur les séries hypergéométriques et sur quelques fonctions qui s'y rattachent, Paris, Hermann 1936

literature

• William Fogg Osgood A modern French Calculus Bull. Amer. Math. Soc. 9 , (1903), pp. 547-555. (English)
• William Fogg Osgood Review: Edouard Goursat, A Course in Mathematical Analysis Bull. Amer. Math. Soc. 12 , (1906), p. 263. (English)

Web links

• Literature by and about Édouard Goursat in the catalog of the German National Library
• John J. O'Connor, Edmund F. Robertson :  Édouard Goursat. In: MacTutor History of Mathematics archive .