A key theorem of calculus of variations is the Euler-Lagrange equation. This corresponds to the stationary trouble in the functional. When in the outbreak of searching for the maximthe & minima of a work, the analysis of chickenfeed around a supposed guide gives a trouble, to foremost choose. It can't tell of these directly whether the utmost or even even minimum (or neither) has been encountered.

Variational methods come crucial within theoretical physics: in Lagrangian mechanics and in application of the principle of stationary action to quantum mechanics. Variational methods provide a mathematical basis for the finite element method, which is a super right thing for solving boundary value problems. It is besides very much utilized for researching lesson equilibria within materials science, and inside pure math, for instance a apply of the Dirichlet principle for harmonic functions by Bernhard Riemann.

A equivalent lesson could come out under more headings, like Hilbert space techniques, Morse theory, or symplectic geometry. A term variational is utilized of completely extremal functional questions. A survey of geodesics in differential geometry is a field with an perceptible variational content. Lot act has been done on the minimal surface (soap bubble) problem, called Plateau's problem.

A theory of optimal control is a generalization of the calculus of variations.