# Person: Goursat, Édouard Jean-Baptiste

Édouard Goursat was a French mathematician who is best known for his version of the Cauchy-Goursat theorem stating that the integral of a function round a simple closed contour is zero if the function is analytic inside the contour.

### Mathematical Profile (Excerpt):

• This was an unusually short time to prepare for these highly competitive entrance examinations, but Goursat was successful and began his studies at the École in 1876.
• Goursat began a lifelong association and friendship with Émile Picard who was a fellow student in Goursat's first year of study, then became an assistant at the École during Goursat's second year.
• It was Émile Picard who saw that Goursat had great potential to become a university teacher and he encouraged Goursat in that direction.
• Goursat had an inspired collection of teachers at École Normale Supérieure and they added to the encouragement given by Picard.
• But others such as Claude Bouquet and Charles Briot also provided role models that Goursat assimilated into the teaching style that he developed.
• The Cauchy-Goursat theorem states the integral of a function round a simple closed contour is zero if the function is analytic inside the contour.
• Goursat removed this extra condition in Démonstration du théorèm de Cauchy Ⓣ(Demonstration of Cauchy's theorem) (1884).
• Goursat introduced the notion of orthogonal kernels and semiorthogonals in connection with Erik Fredholm's work on integral equations.
• He also remarks that Goursat used differential forms to state and prove Poincaré's lemma for arbitrary order forms and its converse.
• In 1891 Goursat wrote Leçons sur l'intégration des équations aux dérivées partielles du premier ordre Ⓣ(Lectures on the integration of partial differential equations of the first order).
• It is almost certain that l'Hôpital's rule, for finding the limit of a rational function whose numerator and denominator tend to zero at a point, is so named because Goursat named the rule after de l'Hôpital in his Cours d'analyse mathématique .
• Despite working on the many new editions of Cours d'analyse mathématique Ⓣ(Course of Mathematical Analysis), Goursat found time to write other texts such as Le problème de Backlund Ⓣ(Backlund's problem) (1925), and Leçons sur les séries hypergéométriques et sur quelles fonctions qui s'y rattachent Ⓣ(Lectures on the hypergeometric series and functions attached to it) (1936).
• Julia, who was Goursat's student, later collaborated with him.
• Goursat received many honours for his outstanding contributions.

Born 21 May 1858, Lanzac, Lot, France. Died 25 November 1936, Paris, France.

View full biography at MacTutor

Analysis, Bourbaki

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### References

#### Adapted from other CC BY-SA 4.0 Sources:

1. O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive