Abstract
The calculus of variations is one of the classical branches of mathematical optimization. It has numerous applications in physics, especially in mechanics. Usually, the problem is to find such a function — from among functions possessing prescribed properties — for which the given integral (functional), whose value depends on these functions, assumes its extremum value. From the geometrical point of view, the problem can be stated as to find such a manifold (curve, surface, hypersurface) in a given class of smooth manifolds that gives the (at least local) minimum or maximum to the given functional, with respect to the class of the manifolds considered.
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© 1994 Springer Science+Business Media New York
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Nožička, F. (1994). Calculus of Variations. In: Survey of Applicable Mathematics. Mathematics and Its Applications, vol 280/281. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8308-4_23
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DOI: https://doi.org/10.1007/978-94-015-8308-4_23
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-015-8310-7
Online ISBN: 978-94-015-8308-4
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