
Accession Number : AD0602166
Title : LECTURES ON APPLIED MATHEMATICS, THE CALCULUS OF VARIATIONS.
Descriptive Note : Research and development rept.,
Corporate Author : DAVID TAYLOR MODEL BASIN WASHINGTON D C
Personal Author(s) : Murnaghan,Francis D.
Report Date : MAY 1961
Pagination or Media Count : 177
Abstract : Contents: The Lagrangian function and the parametric integrand Extremal curves; The EulerLagrange equation Lagrangian functions which are linear in x sub t The Legendre condition for a minimal curve Proof of the Legendre condition Constrained problems; The Hamilton canonical equations The reciprocity between L and H; The transversality conditions Extremal fields; The Hilbert invariant integral The Weierstrass Efunction; Positively regular problems A simple example of the construction of an extremal field; Rayleigh quotients and the method of RayleighRitz The principle of maupertuis; The propagation of waves Problems whose Lagrangian functions involve derivatives of higher order than the first MultipleIntegral problems of the calculus of variations Constrained problems; Characteristic numbers Multipleintegral problems whose Langrangian functions involve derivatives of higher order than the first The Courant maximumminimum principle
Descriptors : (*CALCULUS OF VARIATIONS, THEORY), (*MATHEMATICS, TEXTBOOKS), MECHANICS, ELECTROMAGNETIC RADIATION, PROPAGATION
Distribution Statement : APPROVED FOR PUBLIC RELEASE