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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.
C.G. Gray, G. Karl, and V. A. Novikov, "Progress in Classical and Quantum Variational Principles". 11 December 2003. physics/0312071 Classical Physics. Griffiths, David J. (2004). Introduction to Quantum Mechanics (2nd ed.). Prentice Hall. ISBN 0-13-805326-X. John Venables, "The Variational Principle and some applications". Dept of Physics and ...
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.
Pages in category "Calculus of variations" The following 73 pages are in this category, out of 73 total. ... History of variational principles in physics;
This is a list of variational topics in from mathematics and physics. See calculus of variations for a general introduction. Action (physics) Averaged Lagrangian; Brachistochrone curve; Calculus of variations; Catenoid; Cycloid; Dirichlet principle; Euler–Lagrange equation cf. Action (physics) Fermat's principle; Functional (mathematics ...
Optimal control is an extension of the calculus of variations, and is a mathematical optimization method for deriving control policies. [6] The method is largely due to the work of Lev Pontryagin and Richard Bellman in the 1950s, after contributions to calculus of variations by Edward J. McShane . [ 7 ]
Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus.
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