Charles François Sturm and Differential Equations

Jasper Lützen () and Angelo Mingarelli ()
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Jasper Lützen: University of Copenhagen, Department of Mathematical Sciences
Angelo Mingarelli: Carleton University, School of Mathematics and Statistics

A chapter in Collected Works of Charles François Sturm, 2009, pp 25-47 from Springer

Abstract: Abstract There are several types of innovation in mathematical research: 1) Solutions of problems either in mathematics or outside; 2) Formulations and/or proofs of new mathematical theorems; 3) Developments of new areas and/or methodologies and/or questions. Sturm’s work on equations presents innovations of the first and second type, whereas his work on differential equations primarily presents innovations of the third type. To be sure, Sturm was inspired by problems in physics when he developed his new theories, but his papers did not present the solution of specific problems. It is equally true that his new theories contain several new theorems, some of them later named after him, but they are remarkable primarily because they are of an entirely new kind.

Keywords: Quadratic Form; Real Root; Real Zero; Orthogonality Relation; Liouville Theory (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/978-3-7643-7990-2_3

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