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 Euler-Lagrange 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 E-function; Positively regular problems A simple example of the construction of an extremal field; Rayleigh quotients and the method of Rayleigh-Ritz The principle of maupertuis; The propagation of waves Problems whose Lagrangian functions involve derivatives of higher order than the first Multiple-Integral problems of the calculus of variations Constrained problems; Characteristic numbers Multiple-integral problems whose Langrangian functions involve derivatives of higher order than the first The Courant maximum-minimum principle

Descriptors :   (*CALCULUS OF VARIATIONS, THEORY), (*MATHEMATICS, TEXTBOOKS), MECHANICS, ELECTROMAGNETIC RADIATION, PROPAGATION

Distribution Statement : APPROVED FOR PUBLIC RELEASE