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| {{Infobox scientist
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| |name = Édouard Goursat
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| |image = Goursat_Edouard.jpg
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| |image_size = 160px
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| |caption = Edouard Goursat
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| |birth_date = {{Birth date|1858|05|21|df=y}}
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| |birth_place = [[Lanzac]], [[Lot (département)|Lot]]
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| |death_date = {{Death date and age|1936|11|25|1858|05|21|df=y}}
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| |death_place = [[Paris]]
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| |nationality = French
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| |field = [[Mathematics]]
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| |work_institutions = [[University of Paris]]
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| |alma_mater = [[École Normale Supérieure]]
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| |doctoral_advisor = [[Jean Gaston Darboux]]
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| |doctoral_students = [[Georges Darmois]]<br>[[Dumitru Ionescu]]
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| |known_for = [[Goursat tetrahedron]], [[Goursat's theorem]]
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| |prizes =
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| }}
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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]].<ref>{{cite journal|author=Osgood, W. F.|authorlink=William Fogg Osgood|title=Review: ''Cours d'analyse mathématique''. Tome I.|journal=Bull. Amer. Math. Soc.|year=1903|volume=9|issue=10|pages=547–555|url=http://www.ams.org/journals/bull/1903-09-10/S0002-9904-1903-01028-3/}}</ref><ref>{{cite journal|author=Osgood, W. F.|title=Review: ''Cours d'analyse mathématique''. Tome II.|journal=Bull. Amer. Math. Soc.|year=1908|volume=15|issue=3|pages=120–126|url=http://www.ams.org/journals/bull/1908-15-03/S0002-9904-1908-01704-X/}}</ref> This led to its translation in English by [[Earle Raymond Hedrick]] published by Ginn and Company. Goursat also published texts on [[partial differential equation]]s and [[hypergeometric series]].
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| ==Life==
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| Edouard Goursat was born in [[Lanzac]], [[Lot (département)|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]].
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| ==Work==
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| Goursat was the first to note that the generalized [[Stokes theorem]] can be written in the simple form
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| :<math>\int_S \omega = \int_T d \omega </math>
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| where <math>\omega</math> 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 <math>\omega</math> is a ''p''-form, then <math>d\omega=0</math> if and only if there is a (''p'' − 1)-form <math>\eta</math> with
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| <math>d \eta=\omega</math>. However Goursat did not notice that the "only if" part of the result depends on the domain of <math>\omega</math> 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.
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| ==Books by Edouard Goursat==
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| * [http://www.archive.org/details/coursemathanalys01gourrich A Course In Mathematical Analysis Vol I] Translated by O. Dunkel and E. R. Hedrick (Ginn and Company, 1904)
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| * [http://www.archive.org/details/coursemathema0102gourrich A Course In Mathematical Analysis Vol II, part I] Translated by O. Dunkel and E. R. Hedrick (Ginn and Company, 1916) (Complex analysis)
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| * [http://www.archive.org/details/differentalequat033197mbp A Course In Mathematical Analysis Vol II Part II] Translated by O. Dunkel and E. R. Hedrick (Ginn and Company, 1917) (Differential Equations)
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| * [http://name.umdl.umich.edu/ACR1803.0001.001 Leçons sur l'intégration des équations aux dérivées partielles du premier ordre] (Hermann, Paris, 1891)<ref name="LovettReview">{{cite journal|author=Lovett, Edgar Odell|authorlink=Edgar Odell Lovett|title=Review: Goursat's Partial Differential Equations|journal=Bull. Amer. Math. Soc.|year=1898|volume=4|issue=9|pages=452–487|url=http://www.ams.org/journals/bull/1898-04-09/S0002-9904-1898-00540-2/}}</ref>
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| * [http://gallica.bnf.fr/document?O=N084146 Leçons sur l'intégration des équations aux dérivées partielles du second ordre, à deux variables indépendantes Tome 1] (Hermann, Paris 1896–1898)<ref name=LovettReview/>
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| * [http://gallica.bnf.fr/document?O=N084147 Leçons sur l'intégration des équations aux dérivées partielles du second ordre, à deux variables indépendantes Tome 2] (Hermann, Paris 1896–1898)<ref name=LovettReview/>
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| * [http://gallica.bnf.fr/document?O=N038309 Leçons sur les séries hypergéométriques et sur quelques fonctions qui s'y rattachent] (Hermann, Paris, 1936–1939)<ref>{{cite journal|author=Szegő, G.|authorlink=Gábor Szegő|title=Review: ''Leçons sur les séries hypergéométriques et sur quelques fonctions qui s'y rattachent'' by É. Goursat|journal=Bull. Amer. Math. Soc.|year=1938|volume=44|issue=1, Part 1|page=16|url=http://www.ams.org/journals/bull/1938-44-01/S0002-9904-1938-06654-2/S0002-9904-1938-06654-2.pdf}}</ref>
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| * [http://gallica.bnf.fr/document?O=N038954 Le problème de Bäcklund] (Gauthier-Villars, Paris, 1925)
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| * [http://gallica.bnf.fr/document?O=N099552 Leçons sur le problème de Pfaff] (Hermann,Paris, 1922)<ref>{{cite journal|author=Dresden, Arnold|authorlink=Arnold Dresden|title=Review: ''Leçons sur le problème de Pfaff''|journal=Bull. Amer. Math. Soc.|year=1924|volume=30|issue=7|pages=359–362|url=http://www.ams.org/journals/bull/1924-30-07/S0002-9904-1924-03903-2/}}</ref>
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| * [http://gallica.bnf.fr/document?O=N099595 Théorie des fonctions algébriques et de leurs intégrales : étude des fonctions analytiques sur une surface de Riemann] with [[Paul Appell]] (Gauthier-Villars, Paris, 1895)<ref>{{cite journal|author=Osgood, W. F.|title=Review: ''Théorie des fonctions algébriques et de leurs intégrales'', by P. Appell and É. Goursat|journal=Bull. Amer. Math. Soc.|year=1896|volume=2|issue=10|pages=317–327|url=http://www.ams.org/journals/bull/1896-02-10/S0002-9904-1896-00353-0/}}</ref>
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| * [http://gallica.bnf.fr/document?O=N092706 Théorie des fonctions algébriques d'une variable et des transcendantes qui s'y rattachent Tome II, Fonctions automorphes] with Paul Appell (Gauthier-Villars, 1930)
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| ==See also==
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| *[[Goursat problem]]
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| *[[Goursat tetrahedron]]
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| *[[Goursat's lemma]]
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| ==References==
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| {{reflist}}
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| * {{Cite book|first=Victor |last=Katz |title=A History of Mathematics: An introduction |edition=3rd |publisher=Addison-Wesley |location=Boston |year=2009 |isbn=978-0-321-38700-4 }}
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| ==External links==
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| * {{MacTutor Biography|id=Goursat}}
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| * William Fogg Osgood [http://projecteuclid.org/euclid.bams/1183417526 A modern French Calculus] Bull. Amer. Math. Soc. '''9''', (1903), pp. 547–555.
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| * William Fogg Osgood [http://projecteuclid.org/euclid.bams/1183418774 Review: Edouard Goursat, A Course in Mathematical Analysis] Bull. Amer. Math. Soc. '''12''', (1906), p. 263.
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| *{{MathGenealogy |id=96283}}
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| {{Authority control|VIAF=61605699}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME =Goursat, Edouard
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = French mathematician
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| | DATE OF BIRTH =21 May 1858
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| | PLACE OF BIRTH =[[Lanzac]], [[Lot (département)|Lot]]
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| | DATE OF DEATH =25 November 1936
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| | PLACE OF DEATH = [[Paris]]
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| }}
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| {{DEFAULTSORT:Goursat, Edouard}}
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| [[Category:1858 births]]
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| [[Category:1936 deaths]]
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| [[Category:19th-century French mathematicians]]
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| [[Category:20th-century mathematicians]]
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| [[Category:Mathematical analysts]]
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| [[Category:École Normale Supérieure alumni]]
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| [[Category:University of Paris faculty]]
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