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Édouard Jean-Baptiste Goursat (21 May 1858 – 25 November 1936) was a French mathematician, now remembered principally as an expositor for his Cours d'analyse mathématique, which appeared in the first decade of the twentieth century. It set a standard for the high-level teaching of mathematical analysis, especially complex analysis. This text was reviewed by William Fogg Osgood for the Bulletin of the American Mathematical Society.[1][2] This led to its translation in English by Earle Raymond Hedrick published by Ginn and Company. Goursat also published texts on partial differential equations and hypergeometric series.

Édouard Goursat
Goursat Edouard.jpg
Edouard Goursat
Born(1858-05-21)21 May 1858
Died25 November 1936(1936-11-25) (aged 78)
NationalityFrench
Alma materÉcole Normale Supérieure
Known forGoursat tetrahedron, Cauchy–Goursat theorem, Goursat's lemma
Scientific career
FieldsMathematics
InstitutionsUniversity of Paris
Doctoral advisorJean Gaston Darboux
Doctoral studentsGeorges Darmois
Dumitru Ionescu [ro]

LifeEdit

Edouard Goursat was born in Lanzac, Lot. He was a graduate of the École Normale Supérieure, where he later taught and developed his Cours. At that time the topological foundations of complex analysis were still not clarified, with the Jordan curve theorem considered a challenge to mathematical rigour (as it would remain until L. E. J. Brouwer took in hand the approach from combinatorial topology). Goursat's work was considered by his contemporaries, including G. H. Hardy, to be exemplary in facing up to the difficulties inherent in stating the fundamental Cauchy integral theorem properly. For that reason it is sometimes called the Cauchy–Goursat theorem.

WorkEdit

Goursat was the first to note that the generalized Stokes theorem can be written in the simple form

 

where   is a p-form in n-space and S is the p-dimensional boundary of the (p + 1)-dimensional region T. Goursat also used differential forms to state the Poincaré lemma and its converse, namely, that if   is a p-form, then   if and only if there is a (p − 1)-form   with  . However Goursat did not notice that the "only if" part of the result depends on the domain of   and is not true in general. E. Cartan himself in 1922 gave a counterexample, which provided one of the impulses in the next decade for the development of the De Rham cohomology of a differential manifold.

Books by Edouard GoursatEdit

See alsoEdit

ReferencesEdit

  1. ^ Osgood, W. F. (1903). "Review: Cours d'analyse mathématique. Tome I." Bull. Amer. Math. Soc. 9 (10): 547–555. doi:10.1090/s0002-9904-1903-01028-3.
  2. ^ Osgood, W. F. (1908). "Review: Cours d'analyse mathématique. Tome II". Bull. Amer. Math. Soc. 15 (3): 120–126. doi:10.1090/s0002-9904-1908-01704-x.
  3. ^ a b c Lovett, Edgar Odell (1898). "Review: Goursat's Partial Differential Equations". Bull. Amer. Math. Soc. 4 (9): 452–487. doi:10.1090/S0002-9904-1898-00540-2.
  4. ^ Szegő, G. (1938). "Review: Leçons sur les séries hypergéométriques et sur quelques fonctions qui s'y rattachent by É. Goursat" (PDF). Bull. Amer. Math. Soc. 44 (1, Part 1): 16–17. doi:10.1090/s0002-9904-1938-06652-9.
  5. ^ Dresden, Arnold (1924). "Review: Leçons sur le problème de Pfaff". Bull. Amer. Math. Soc. 30 (7): 359–362. doi:10.1090/s0002-9904-1924-03903-2.
  6. ^ Osgood, W. F. (1896). "Review: Théorie des fonctions algébriques et de leurs intégrales, by P. Appell and É. Goursat". Bull. Amer. Math. Soc. 2 (10): 317–327. doi:10.1090/s0002-9904-1896-00353-0.
  • Katz, Victor (2009). A History of Mathematics: An introduction (3rd ed.). Boston: Addison-Wesley. ISBN 978-0-321-38700-4.

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