LECTURES ON APPLIED MATHEMATICS, THE CALCULUS OF VARIATIONS
Research and development rept.
DAVID TAYLOR MODEL BASIN WASHINGTON DC
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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
- Numerical Mathematics