The inverse problem of the calculus of variations: An operator-theoretic study

The inverse problem of the calculus of variations is examined from an operator-theoretic point of view instead of as an integration problem. These operators give a convenient, presentation of generalizations to higher order Lagrangians. Original material on this subject will be found in chapter four. The Noether theorem is discussed and the operators developed in chapter three appear in this setting.;To provide some insight and justification for considering the Euler-Lagrange expressions as operators, chapter two compares these expressions to the familiar gradient of vector calculus.;As an aid to calculation and to provide an elegant presentation of the calculus of variations, chapter one considers the foundations of the exterior algebra and the theory of differential forms which uses this algebra.