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Fundamental equation in the calculus of variations used to find functions that minimize or maximize functionals.

Method used to find the extrema of functionals subject to equality constraints.

A measure of how a functional changes when the function it depends on is varied, serving as the basis for the calculation of variations.

A variational principle that states that certain boundary value problems can be solved by minimizing an associated energy functional.

The path taken by the system between two states is the one for which the action integral is a minimum.

States that the actual motion of a dynamic system is such that the action integral is stationary (no variation) for it compared to nearby motions.

States that every differentiable symmetry of the action of a physical system has a corresponding conservation law.

A method to approximate the eigenvalues and eigenfunctions of an operator, commonly used in quantum mechanics and structural engineering.

Conditions on the boundaries of the domain that a solution to a variational problem must satisfy.

The principle that the path taken between two points by a ray of light is the path that can be traversed in the least time.

Used to optimize functional models in economics, such as utility, cost, or production functionals over time or other variables.

A principle stating that the action does not change for small variations of the path—action is stationary for the path actually followed.

Variational principle used to approximate the ground state of a quantum system.

A form of the Euler-Lagrange equation applicable when the functional being extremized does not explicitly depend on the independent variable.