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 DC

Personal Author(s):

Report Date:

1961-05-01

Pagination or Media Count:

179.0

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 Lagrangian functions involve derivatives of higher order than the first The Courant maximum-minimum principle

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE