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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.
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 . Introduction to the calculus of variations ; Imperial College Press, London (2004), 2nd ed. (2009), 3rd ed (2014); According to WorldCat , the book is held in 882 libraries. [ 4 ]
Giaquinta, Mariano (1983), Multiple integrals in the calculus of variations and nonlinear elliptic systems, Annals of Mathematics Studies, vol. 105, Princeton, New Jersey: Princeton University Press, pp. vii+297, ISBN 0-691-08330-4, MR 0717034, Zbl 0516.49003. Giaquinta, Mariano; Hildebrandt, Stefan (1996), Calculus of
Malliavin calculus is also called the stochastic calculus of variations. P. Malliavin first initiated the calculus on infinite dimensional space. Then, the significant contributors such as S. Kusuoka, D. Stroock, J-M. Bismut, Shinzo Watanabe, I. Shigekawa, and so on finally completed the foundations.
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 δf .
William Gilbert Strang (born November 27, 1934 [1]) is an American mathematician known for his contributions to finite element theory, the calculus of variations, wavelet analysis and linear algebra. He has made many contributions to mathematics education, including publishing mathematics textbooks.
Hanno Rund (26 October 1925 in Schwerin – 5 January 1993 in Tucson, Arizona) was a German mathematician. [1] He wrote numerous publications, including perhaps his most famous, The Hamilton-Jacobi theory in the calculus of variations.
Download as PDF; Printable version; ... calculus of variations and partial differential equations. ... was published as a book in 2017 by Edizioni della Normale. ...