Eugène Rouché (1832 to 1910) was a French mathematician, born on 18 August 1832 and an alumnus of the Ecole Polytechnique, which he entered in 1852. He became professor of mathematics at the Charlemagne lyceum and then at the Ecole Centrale, and served as an admissions examiner at the Ecole Polytechnique. He is best known for Rouché's theorem in complex analysis, which he published in the school's journal in 1862, and for the Rouché-Capelli theorem in linear algebra. With Comberousse he wrote a treatise on geometry that had reached its seventh edition by 1900. His son Jacques was a noted patron of the arts who managed the Paris Opera for thirty years. He died on 19 August 1910.
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Source Eugène Rouché (Wikipedia)
Principal Result
Source Eugène Rouché (Wikipedia)
Proofs Credited
Source Rouche's Theorem (Wikipedia)
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Source Eugène Rouché (Wikipedia)LeadQuote, Lead
was a French mathematician.
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1. MacTutor History of Mathematics: Eugène Rouché (MacTutor)
MacTutor History of MathematicsBiography
He attended the school at the same time as Gustave Eiffel
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18 August 1832
View the Source Eugène Rouché (Wikipedia)
Lead
was a French mathematician.
In Branch: Complex Analysis, Career
He is best known for Rouché's theorem in complex analysis
Principal Result: Rouche's Theorem, Career, Rouche theorem
He is best known for Rouché's theorem in complex analysis
View the SourceRouche's Theorem (Wikipedia)
Proofs Credited: Rouche's Theorem, Lead sentenceQuote, Proofs Credited: Rouche's Theorem, Lead sentence
Rouché's theorem, named after Eugène Rouché, states that for any two complex-valued functions f and g holomorphic inside some region K {\displaystyle K} with closed contour ∂ K {\displaystyle \partial K} , if |g(z)| < |f(z)| on ∂ K {\displaystyle \partial K} , then f and f + g have the same number of zeros inside K {\displaystyle K} , where each zero is counted as many times as its multiplicity.
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