Complete Works of Charles-François Sturm by Jean-Claude Pont, Flavia Padovani

By Jean-Claude Pont, Flavia Padovani

Charles Fran?ois Sturm was once born in Geneva, Switzerland, on September 29, 1803. He got his medical schooling during this urban and started his wealthy clinical occupation there via major learn in sound propagation and compressibility of fluids. In September of 2003, at the party of the 2 hundredth anniversary of his start, his domestic urban honoured his around the world acceptance with a colloquium and workshop less than the sponsorship of the collage of Geneva.

This quantity relies on lectures awarded at that colloquium, which thinking about C.F. Sturm's personal paintings. The ebook incorporates a collection of reproductions of his medical guides. Sturm contributed significantly to geometry (theory of polygons, effortless geometry, projective geometry, conic sections), algebra, research (differential equations, series), optics (caustics, physiological optics), mechanics, and different components of physics (particularly fluid mechanics and velocity of sound in water).

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When he was promoted to professor in 1838 he chose the senior Sturm as his répétiteur and when Sturm was promoted to professor two years later the two friends taught the course in alternate years for the next decade. At the Académie des Sciences they helped each other to be elected, this time in order of age. They both presented themselves as candidates in 1833 together with their common friend Duhamel and the Italian mathematician Libri-Carucci, but at this occasion Libri was elected member. In 1836 the three friends tried again.

L’identité structurelle du théorème de Sturm avec des théorèmes importants démontrés pour le cas complexe, tels que le théorème sur le résultant d’une suite finie de polynômes ou le théorème des zéros de Hilbert, devient claire. Rétrospectivement, nous gagnons une compréhension renouvelée du lien intime de l’Analyse classique avec un usage correct des quantificateurs universel et existentiel, comme il s’en présente dans l’énoncé de théorèmes tels que ceux sur la continuité ou la convergence (uniformes) de fonctions.

When Sturm died in 1855, Liouville gave a moving speech at the grave on behalf of the Académie des Sciences, ending with the words: Ah! cher ami, ce n’est pas toi qu’il faut plaindre. Echappée aux angoisses de cette vie terrestre, ton âme immortelle et pure habite en paix dans le sein de Dieu, et ton nom vivra autant que la science. Adieu, Sturm, adieu. [Liouville 1855] Two months later when he wrote to his friend Dirichlet, he was still mourning: Venez et vous serez le bien venu. Nous pleurons ensemble notre pauvre Sturm.

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