High Quality Content by WIKIPEDIA articles! In the calculus of variations the Legendre-Clebsch condition is a second-order condition which a solution of the Euler-Lagrange equation must satisfy in order to be a maximum (and not a minimum or another kind of extremal). Calculus of variations is a field of mathematics that deals with functionals, as opposed to ordinary calculus which deals with functions. Such functionals can for example be formed as integrals involving an unknown function and its derivatives. The interest is in extremal functions – those making the functional attain a maximum or minimum value – or stationary functions – those where the rate of change of the functional is precisely zero.

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