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High Quality Content by WIKIPEDIA articles! In mathematics, a difference operator maps a function, (x), to another function, (x + b) (x + a). The forward difference operator Delta f(x)=f(x+1)-f(x), occurs frequently in the calculus of finite differences, where it plays a role formally similar to that of the derivative, but used in discrete circumstances. Difference equations can often be solved with techniques very similar to those for solving differential equations. This similarity led to the development of time scale calculus. Analogously we can have the backward difference operator