Editing Calculus of variations (section)

=== Further applications ===

Further applications of the calculus of variations include the following:

* The derivation of the [[catenary]] shape
* Solution to [[Newton's minimal resistance problem]]
* Solution to the [[Brachistochrone curve|brachistochrone]] problem
* Solution to the [[Tautochrone curve|tautochrone problem]]
* Solution to [[isoperimetric]] problems
* Calculating [[geodesic]]s
* Finding [[minimal surface]]s and solving [[Plateau's problem]]
* [[Optimal control]]
* [[Analytical mechanics]], or reformulations of Newton's laws of motion, most notably [[Lagrangian mechanics|Lagrangian]] and [[Hamiltonian mechanics]];
* Geometric optics, especially Lagrangian and [[Hamiltonian optics]];
* [[Variational method (quantum mechanics)]], one way of finding approximations to the lowest energy eigenstate or ground state, and some excited states;
* [[Variational Bayesian methods]], a family of techniques for approximating intractable integrals arising in Bayesian inference and machine learning;
* [[Variational methods in general relativity]], a family of techniques using calculus of variations to solve problems in Einstein's general theory of relativity;
* [[Finite element method]] is a variational method for finding numerical solutions to boundary-value problems in differential equations;
* [[Total variation denoising]], an [[image processing]] method for filtering high variance or noisy signals.