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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Beltrami identity is an identity in the calculus of variations. 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.