# 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

# Descriptors:

# Subject Categories:

- Numerical Mathematics