ABSTRACT
In this paper we show how the umbral calculus appears in a natural way when one is dealing with linear discrete equations on uniform lattices and at the same time wants to preserve the symmetries of the continuous case independently of the discrete derivative involved. We implement the umbral calculus to q-difference equations and work out, as an example, the symmetries of the q-heat equation and use some of them to get an explicit solution the q-heat equation.
