The Calculus of Variations
1st Edition
Published on 1. January 1988
Book
Hardback
280 pages
978-3-7186-4805-4 (ISBN)
Description
An authoritative text on the calculus of variations for first-year graduate students. From a study of the simplest problem it goes on to cover Lagrangian derivatives, Jacobi's condition, and field theory. Devotes considerable attention to direct methods and the Sturm-Liouville problem in a finite interval. Contains numerous interesting and challenging exercises plus five appendices on important results, generalizations, and applications of the material,
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Content
The simplest problem; lagrangian derivatives; canonical variables; field theory; Jacobi's condition; the simplest problem in parametric form; problems on a conditional extremum; the direct method for nonparametric problems; the Sturm-Liouville problem; the direct method for a problem in parametric form; two-demensional problems; the generalized dirichlet problem for a linear equation of elliptic type; S.N.Bernshtein's principle; geodesic lines on a triaxial ellipsoid; Poincare's theorem on periodic extremals; E.Noether's theorem on invariant functionals.