Collected Works of Charles François Sturm (English and French Edition)

Charles François Sturm was born in Geneva, Switzerland, on September 29, 1803. He obtained his scientific education in this city and began his rich scientific career there through significant research in sound propagation and compressibility of fluids. In September of 2003, on the occasion of the 200th anniversary of his birth, his home city honoured his worldwide recognition with a colloquium and workshop under the sponsorship of the University of Geneva. This volume is based on lectures presented at that colloquium, which focused on C.F. Sturm's own work. The book contains a selection of reproductions of his scientific publications. Sturm contributed notably to geometry (theory of polygons, elementary geometry, projective geometry, conic sections), algebra, analysis (differential equations, series), optics (caustics, physiological optics), mechanics, and other areas of physics (particularly fluid mechanics and speed of sound in water). These original papers are accompanied by contributions from internationally renowned experts who have worked on and deepened understanding of many topics of interest to Sturm, in particular differential equations, optics and algebraic curves. The volume complements the book __Sturm-Liouville Theory. Past and Present__ (ISBN 978-3-7643-7066-4) that also originates from that colloquium. Front Matter....Pages i-x Charles François Sturm: notice biographique....Pages 1-11 L’Œuvre algébrique de Charles François Sturm....Pages 13-24 Charles François Sturm and Differential Equations....Pages 25-47 Charles François Sturm’s Writings on Optics....Pages 49-65 Mécanique....Pages 67-110 Compressibilite des liquides et vitesse un son....Pages 111-114 Front Matter....Pages 115-115 Solution du problème de dynamique énoncé à la page 180 du présent volume....Pages 117-131 Solution partielle du problème de géométrie énoncé à la page 288 du XII e volume du présent recueil....Pages 132-136 Démonstration d’un théorème de géoméirie; énoncé à la page 248 du précédent volume....Pages 137-140 Démonstration de deux théorèmes de géométrie, énoncés à la page 248 du XIII: volume des Annales....Pages 141-147 Recherehes analitiques, sur une classe de problèmes de géométrie dépendant de la théorie des maxima et minima....Pages 148-158 Démonstration des deux théorèmes de géométrie énoncés à la page 63 du présent volume....Pages 160-165 Autre démonstration du même théorème....Pages 166-173 Solulion du dernier des quatre problèmes de géométrie proposés a la page 304 du précédent volume....Pages 174-179 Solution du problème de statique énoncé à la page 28 du présent volume....Pages 181-189 Addition à l’article inséré à la page 286 du présent volume....Pages 190-191 Démonstration des quatre théorèmes sur l’hyperbole énoncés à la page 268 du précédent volume....Pages 192-196 Recherches sur les caustiques....Pages 197-210 Théorèmes sur les polygones réguliers....Pages 212-218 Recherches analitiques sur les polygones reclilignes plans ou gauches, renfermant la solution de plusieurs questions proposées dans le présent recueil....Pages 219-254 Front Matter....Pages 115-115 Recherches d’analise sur les caustiques planes....Pages 256-265 Mémoire sur les lignes du second ordre....Pages 267-295 Mémoire sur les lignes du second ordre....Pages 297-322 Analyse d’ un Mémoire sur la résolution des équations numériques....Pages 323-326 Extrait d’un Mémoire de M. Sturm, présenté à l’Académie des sciences....Pages 328-331 Note présentée à l’ Acurlémie....Pages 333-333 Extrait d’un Mémoire sur L’intécration d’un système d’équations différentielles linéaires, présenté à l’Académie des sciences....Pages 334-342 M. Cauchy fait le Rapport suivent sur le Mémoire de M. Sturm, intitulé Résumé d’une nouvelle théorie relative à une classe de fonctions transcendantes....Pages 343-344 Mémoire sur la résolution des équations numériques....Pages 345-390 Mémoire Sur les Equations différentielles linéaires du second ordre....Pages 392-472 Démonstration D’un Théorème de M. Cauchy relatif aux racines imaginaires des Equations....Pages 474-485 Autres démonstrations du même Théorème....Pages 486-504 Mémoire Sur une classe d’Équations à différences partielles....Pages 505-576 Note sur un théorème de M. Cauchy relatif aux racines des équations simultanées....Pages 578-582 Extrait D’un Mémoire sur le développement des fonctions en séries dont les différents termes sont assujettis à satisfaire à une méme équation différentielle linéaire, contenant un paramètre variable....Pages 584-587 Mémoire sur La comperssion des liquides....Pages 589-669 Mémoire sur L’optique....Pages 671-698 Note de M. Sturm, relative au Mémoire de M. Libri inséré dans le précédent Compte rendu....Pages 700-700 Réponse de M. Libri à la Note de M. Sturm....Pages 701-702 Mémoire sur quelques propositions de mécanique rationnelle....Pages 704-709 Front Matter....Pages 115-115 Note de M. Sturm, à l’occasion de l’article précédent....Pages 711-716 Note de M. Sturm, à l’occasion de l’article, précédent....Pages 718-719 Note Sur un Mémoire de M. Chasles....Pages 721-731 Démonstration d’un Théorème d’algèbre de M. Sylvester....Pages 732-744 Mémoire sur la théorie de la vision....Pages 746-779 Note sur l’intégration des équations générales de la dynamique....Pages 780-788 Sur le mouvement d’un corps solide autour d’us point fixe....Pages 789-802 Back Matter....Pages 803-808 This is a collection of survey articles based on lectures presented at a colloquium and workshop in Geneva in 2003 to commemorate the 200th anniversary of the birth of Charles François Sturm. It aims at giving an overview of the development of Sturm-Liouville theory from its historical roots to present day research. It is the first time that such a comprehensive survey is made available in compact form. The contributions come from internationally renowned experts and cover a wide range of developments of the theory. The book can therefore serve both as an introduction to Sturm-Liouville theory and as background for ongoing research. The text is particularly strong on the spectral theory of Sturm-Liouville equations, which has given rise to a major branch of modern analysis. Among other current aspects of the theory discussed are oscillation theory for differential equations and Jacobi matrices, approximation of singular boundary value problems by regular ones, applications to systems of differential equations, extension of the theory to partial differential equations and to non-linear problems, and various generalizations of Borg's inverse theory. A unique feature of the book is a comprehensive catalogue of Sturm-Liouville differential equations covering more than fifty examples, together with their spectral properties. Many of these examples are connected with special functions and with problems in mathematical physics and applied mathematics. The volume is addressed to researchers in related areas, to advanced students and to those interested in the historical development of mathematics. The book will also be of interest to those involved in applications of the theory to diverse areas such as engineering, fluid dynamics and computational spectral analysis "Charles Francois Sturm was born in Geneva, Switzerland, on September 29, 1803. He obtained his scientific education in this city and began his rich scientific career there through significant research in sound propagation and compressibility of fluids. In September of 2003, on the occasion of the 200th anniversary of his birth, his home city honoured his worldwide recognition with a colloquium and workshop under the sponsorship of the University of Geneva." "This volume is based on lectures presented at that colloquium, which focused on C.F. Sturm's own work. The book contains a selection of reproductions of his scientific publications. Sturm contributed notably to geometry (theory of polygons, elementary geometry, projective geometry, conic sections), algebra, analysis (differential equations, series), optics (caustics, physiological optics), mechanics, and other areas of physics (particularly fluid mechanics and speed of sound in water)." "These original papers are accompanied by contributions from internationally renowned experts who have worked on and deepened understanding of many topics of interest to Sturm, in particular differential equations, optics and algebraic curves. The volume complements the book Sturm-Liouville Theory. Past and Present (ISBN 978-3-7643-7066-4) that also originates from that colloquium."--Jacket

Charles François Sturm was born in Geneva, Switzerland, on September 29, 1803. He obtained his scientific education in this city and began his rich scientific career there through significant research in sound propagation and compressibility of fluids. In September of 2003, on the occasion of the 200th anniversary of his birth, his home city honoured his worldwide recognition with a colloquium and workshop under the sponsorship of the University of Geneva.

This volume is based on lectures presented at that colloquium, which focused on C.F. Sturm's own work. The book contains a selection of reproductions of his scientific publications. Sturm contributed notably to geometry (theory of polygons, elementary geometry, projective geometry, conic sections), algebra, analysis (differential equations, series), optics (caustics, physiological optics), mechanics, and other areas of physics (particularly fluid mechanics and speed of sound in water).

This collection of articles on Sturm-Liouville theory is based on lectures presented at the colloquium and workshop held in Geneva on the occasion of Sturm's 200th anniversary. A historical survey of the field is combined with in-depth coverage of later developments and contemporary research in this major area of modern mathematics and its applications. The authors are among the world's leading experts in this field