LECTURES ON APPLIED MATHEMATICS, THE CALCULUS OF VARIATIONS

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

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 01, 1961
Accession Number
AD0602166

Entities

People

  • Francis D. Murnaghan

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Applied Mathematics
  • Boundary Value Problems
  • Calculus
  • Calculus Of Variations
  • Construction
  • Differential Equations
  • Equations
  • Hamiltonian Functions
  • Integrals
  • Lagrangian Functions
  • Mathematics
  • Mechanics
  • Partial Differential Equations
  • Polynomials
  • Refractive Index
  • Three Dimensional
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis