  In the present paper the classical point symmetry analysis is extended from
partial differential to functional differential equations with functional
derivatives. In order to perform the group analysis and deal with the
functional derivatives we extend the quantities such as infinitesimal
transformations, prolongations and invariant solutions. For the sake of example
the procedure is applied to the continuum limit of the heat equation. The
method can further lead to significant applications in statistical physics and
fluid dynamics.
