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Geometrical Methods in Variational Problems (Hardcover, 1999 ed.)
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Geometrical Methods in Variational Problems (Hardcover, 1999 ed.)
Series: Mathematics and Its Applications, 485
Expected to ship within 12 - 17 working days
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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.
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