Geometrical methods in variational problems
著者
書誌事項
Geometrical methods in variational problems
（Mathematics and its applications, v. 485）
Kluwer Academic, c1999
- タイトル別名
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Геометриуеские методы в вариационныхзада уах
Geometriueskie metody v variat︠s︡ionnykh zada uakh
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注記
Includes bibliographical references (p. [507]-532) and index
"Original Russian work Геометриуеские методы в вариационных зада уах by N.A. Bobylev, S.V. Emel'yanov and S.K. Korovin, Magister, Moscow 1998" -- T.p. verso
内容説明・目次
内容説明
Since the building of all the Universe is perfect and is cre- ated by the wisdom Creator, nothing arises in the Universe in which one cannot see the sense of some maXImum or mInImUm Euler God moves the Universe along geometrical lines Plato Mathematical models of most closed physical systems are based on vari- ational principles, i.e., it is postulated that equations describing the evolu- tion of a system are the Euler~Lagrange equations of a certain functional. In this connection, variational methods are one of the basic tools for studying many problems of natural sciences. The first problems related to the search for extrema appeared as far back as in ancient mathematics. They go back to Archimedes, Appolonius, and Euclid. In many respects, the problems of seeking maxima and minima have stimulated the creation of differential calculus; the variational prin- ciples of optics and mechanics, which were discovered in the seventeenth and eighteenth centuries, gave impetus to an intensive development of the calculus of variations. In one way or another, variational problems were of interest to such giants of natural sciences as Fermat, Newton, Descartes, Euler, Huygens, 1.
Bernoulli, J. Bernoulli, Legendre, Jacobi, Kepler, La- grange, and Weierstrass.
目次
Preface. 1. Preliminaries. 2. Minimization of Nonlinear Functionals. 3. Homotopic Methods in Variational Problems. 4. Topological Characteristics of Extremals of Variational Problems. 5. Applications. Bibliographical Comments. References. Index.
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