Geometrical Methods in Variational Problems

Bobylov, Nikolai A.; Emel'yanov, S.V. (Institute of Systems Analysis, Moscow, Russia); Korovin, Sergey K.

ISBN 10: 0792357809 / ISBN 13: 9780792357803

Editore: Kluwer Academic Publishers, 1999

This monograph presents methods for the investigation of nonlinear variational problems, based on geometric and topological ideas. Attention is also given to applications in optimization, mathematical physics, control, and numerical methods. Series: Mathematics and its Applications. Num Pages: 543 pages, biography. BIC Classification: PBKQ. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 244 x 170 x 31. Weight in Grams: 962. . 1999. Hardback. . . . . Codice articolo V9780792357803

Riassunto:

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.

Recensione: "... the book is a valuable contribution to the literature. It is well-written, self-contained and it has an extensive bibliography, especially with regard to the literature in the Russian language."
(Mathematical Reviews, 2001a)

Dati bibliografici

Titolo: Geometrical Methods in Variational Problems
Casa editrice: Kluwer Academic Publishers
Data di pubblicazione: 1999
Legatura: Rilegato
Condizione: New