Jean-Gaston Darboux (August 14, 1842, Nîmes – February 23, 1917, Paris) was a French mathematician.

Life

Darboux made several important contributions to geometry and mathematical analysis (see linear PDEs for example). He was a biographer of Henri Poincaré and he edited the Selected Works of Joseph Fourier.

Darboux received his Ph.D. from the École Normale Supérieure in 1866. His thesis, written under the direction of Michel Chasles, was titled Sur les surfaces orthogonales. In 1884, Darboux was elected to the Académie des Sciences. In 1900, he was appointed the Academy's permanent secretary of its Mathematics section.

Among his students were Émile Borel, Élie Cartan, Gheorghe Ţiţeica and Stanisław Zaremba.

Darboux's contribution to the differential geometry of surfaces appears in the four volume collection of studies he published between 1887 and 1896; see links below for access to these texts.

In 1902, he was elected to the Royal Society; in 1916, he received the Sylvester Medal from the Society.

There are many things named after him:

* Darboux equation

* Darboux frame

* Darboux integral

* Darboux net invariants

* Darboux problem

* Darboux's theorem in symplectic geometry

* Darboux's theorem in real analysis, related to Intermediate value theorem

* Christoffel-Darboux identity[1]

* Christoffel-Darboux formula[2]

* Darboux's formula[3]

* Darboux vector[4]

* Euler-Darboux equation[5]

* Euler-Poisson-Darboux equation[6]

* Darboux cubic[7]

* Darboux[8] or Goursat problem[9]

* Darboux transformation

Books by Gaston Darboux

1887-96. Leçons sur la théorie générale des surfaces et les applications géométriques du calcul infinitésimal. Gauthier-Villars:

* Vol. 1.

* Vol. 2.

* Vol. 3.

* Vol. 4.

See also

* Envelope theorem

Notes

1. ^ Christoffel-Darboux Identity -- from Wolfram MathWorld at mathworld.wolfram.com

2. ^ Christoffel-Darboux Formula -- from Wolfram MathWorld at mathworld.wolfram.com

3. ^ Darboux's Formula -- from Wolfram MathWorld at mathworld.wolfram.com

4. ^ Darboux Vector -- from Wolfram MathWorld at mathworld.wolfram.com

5. ^ Euler-Darboux Equation -- from Wolfram MathWorld at mathworld.wolfram.com

6. ^ Euler-Poisson-Darboux Equation -- from Wolfram MathWorld at mathworld.wolfram.com

7. ^ Darboux Cubic -- from Wolfram MathWorld at mathworld.wolfram.com

8. ^ Darboux Problem -- from Wolfram MathWorld at mathworld.wolfram.com

9. ^ Goursat Problem -- from Wolfram MathWorld at mathworld.wolfram.com

References

* "Darboux, Jean-Gaston". Biographical Dictionary of Mathematicians. Charles Scribner's Sons. 1991.

* Lebon, Ernest (1910). Gaston Darboux. Gauthier-Villars.

* Fourier, Joseph (1888–1890). Œuvres de Fourier. Paris: Gauthier-Villars. ISBN 2051005788. http://gallica.bnf.fr/ark:/12148/bpt6k33707.

External links

* A biography in Weisstein's World of Biography

* O'Connor, John J.; Robertson, Edmund F., "Jean Gaston Darboux", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Darboux.html .

* Jean Gaston Darboux at the Mathematics Genealogy Project

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