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The calculus of variations is a field of mathematical analysis that uses variations,
which are small changes in functions and functionals,
to find maxima and minima of functionals:
mappings from a set of functions to the real numbers.[a]

Functionals are often expressed as definite integrals involving functions
and their derivatives.
Functions that maximize or minimize functionals may be found using
the Euler–Lagrange equation of the calculus of variations.