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 Calculus`VariationalMethods` The basic problem of the calculus of variations is to determine the function that extremizes a functional . In general, there can be more than one independent variable and the integrand can depend on several functions and their higher derivatives. The extremal functions are solutions of the Euler(-Lagrange) equations that are obtained by setting the first variational derivatives of the functional with respect to each function equal to zero. Since many ordinary and partial differential equations that occur in physics and engineering can be derived as the Euler equations for appropriate functionals, variational methods are of general utility. First variational derivatives and Euler equations. VariationalD gives the first variational derivatives of a functional defined by the integrand . may depend on several functions ; their derivatives of arbitrary order; and variables . EulerEquations returns the Euler(-Lagrange) equations given the integrand . Again may depend on several functions ; their derivatives of arbitrary order; and variables . This loads the package. In[1]:= <