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Calculus of variations is concerned with variations of functionals, which are small changes in the functional's value due to small changes in the function that is its argument. The first variation [ l ] is defined as the linear part of the change in the functional, and the second variation [ m ] is defined as the quadratic part.
In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not a single point. . Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function
Download as PDF; Printable version; In other projects Wikimedia Commons; Wikidata item; Appearance. ... Direct method in the calculus of variations; Dirichlet energy;
PDF According to WorldCat, the book is held in 419 libraries [2] Direct methods in the calculus of variations; Springer-Verlag, New-York (1989), 2nd ed. (2007). According to WorldCat, the book is held in 625 libraries [3] PDF.
In the calculus of variations, functionals are usually expressed in terms of an integral of functions, their arguments, and their derivatives. In an integrand L of a functional, if a function f is varied by adding to it another function δf that is arbitrarily small, and the resulting integrand is expanded in powers of δf , the coefficient of ...
In the calculus of variations and classical mechanics, the Euler–Lagrange equations [1] are a system of second-order ordinary differential equations whose solutions are stationary points of the given action functional. The equations were discovered in the 1750s by Swiss mathematician Leonhard Euler and Italian mathematician Joseph-Louis Lagrange.
The free PDF copy is made available by the RCIN –Digital Repository of the Scientifics Institutes. Young, L. C. (January 1942), "Generalized Surfaces in the Calculus of Variations", Annals of Mathematics, Second Series, 43 (1): 84–103, doi:10.2307/1968882, JFM 68.0227.03, JSTOR 1968882, MR 0006023, Zbl 0063.09081.
The free PDF copy is made available by the RCIN –Digital Repository of the Scientifics Institutes. Young, L. C. (1969), Lectures on the Calculus of Variations and Optimal Control, Philadelphia–London–Toronto: W. B. Saunders, pp. xi+331, ISBN 9780721696409, MR 0259704, Zbl 0177.37801.
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