Édouard Jean-Baptiste Goursat was a French mathematician who is best known for his version of the Cauchy-Goursat theorem, which states that the integral of a function round a simple closed contour is zero if the function is analytic inside the contour. He was born at Lanzac in the Lot on 21 May 1858 and died in Paris on 25 November 1936. He attended the Collège de Brive-la-Gaillarde, spent a single year at the Lycée Henri IV preparing for the entrance examinations, and began his studies at the École Normale Supérieure in 1876. There he began a lifelong friendship with Émile Picard, and his teachers included Jean Darboux and Charles Hermite.
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In Branch
Source MacTutor biography of Édouard Goursat, St Andrews
Proofs Credited
Source Cauchy Integral Theorem (Wikipedia)
Source Inverse Function Theorem (Wikipedia)
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Source MacTutor biography of Édouard Goursat, St AndrewsSummaryQuote, Summary
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.
Sources
1. MacTutor biography of Édouard Goursat, St Andrews
Biography
He then spent one year at the Lycée Henri IV preparing to take the entrance examinations for l'École Normale Supérieure.
In Branch: Complex Analysis, Summary
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.
View the SourceCauchy Integral Theorem (Wikipedia)
Wikimedia FoundationProofs Credited: Goursat's Theorem, Article textQuote, Proofs Credited: Goursat's Theorem, Article text
Cauchy provided this proof, but it was later proven by Goursat without requiring techniques from vector calculus, or the continuity of partial derivatives.
Inverse Function Theorem (Wikipedia)
Wikimedia FoundationProofs Credited: Inverse Function Theorem, Lead sectionQuote, Proofs Credited: Inverse Function Theorem, Lead section
The theorem was first established by Picard and Goursat using an iterative scheme: the basic idea is to prove a fixed point theorem using the contraction mapping theorem.
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