Collected Works of Charles François Sturm by Jean-Claude Pont, Isaac Benguigui (auth.), Prof. Jean-Claude PDF

By Jean-Claude Pont, Isaac Benguigui (auth.), Prof. Jean-Claude Pont (eds.)

ISBN-10: 3764379898

ISBN-13: 9783764379896

ISBN-10: 3764379901

ISBN-13: 9783764379902

Charles François Sturm used to be born in Geneva, Switzerland, on September 29, 1803. He bought his medical schooling during this urban and commenced his wealthy clinical occupation there via major study in sound propagation and compressibility of fluids. In September of 2003, at the party of the two hundredth anniversary of his beginning, his domestic urban honoured his all over the world reputation with a colloquium and workshop below the sponsorship of the collage of Geneva.

This quantity is predicated on lectures provided at that colloquium, which enthusiastic about C.F. Sturm's personal paintings. The ebook features a choice of reproductions of his clinical guides. Sturm contributed particularly to geometry (theory of polygons, trouble-free geometry, projective geometry, conic sections), algebra, research (differential equations, series), optics (caustics, physiological optics), mechanics, and different parts of physics (particularly fluid mechanics and velocity of sound in water).

These unique papers are followed by means of contributions from the world over popular specialists who've labored on and deepened realizing of many subject matters of curiosity to Sturm, particularly differential equations, optics and algebraic curves. the amount enhances the booklet Sturm-Liouville conception. previous and Present (ISBN 978-3-7643-7066-4) that still originates from that colloquium.

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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. Parler d’élimination des quantificateurs, c’est donc bien affirmer la nature algébrique des problèmes élémentaires traditionnellement rapportés à l’Analyse réelle. Aussi l’expression d’«algèbre réelle», originairement employée par Artin et Schreier pour désigner la théorie des corps réels clos et justifiée par eux de manière algébrique, reçoit-elle une nouvelle justification, d’ordre logique celle-là.

In fact their joint papers are among the earliest joint papers in the history of mathematics. Even though they did not continue their collaboration beyond 1836 they continued to help each other in their respective careers: At the École Polytechnique Liouville was appointed répétiteur (assistant) in the course of analysis and mechanics already in 1831. 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.

6 According to this note it was a certain Mr. D (probably Dirichlet) who pointed out this problem to him. 7 The first use of this method which is usually attributed to Picard. 34 Jesper Lützen and Angelo Mingarelli The friendship and collaboration between Sturm and Liouville When Sturm first came to Paris in 1825, Liouville was just beginning his first year of study at the École Polytechnique so they probably did not meet right away. Their earliest approaches to Sturm–Liouville theory from the years 1829 – 30 were so different in their goals and their methods that it is almost certain they were developed independently.

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Collected Works of Charles François Sturm by Jean-Claude Pont, Isaac Benguigui (auth.), Prof. Jean-Claude Pont (eds.)

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