Delta derivative on a time scale

Summary

The delta derivative is the derivative of time-scale calculus, defined for functions on a time scale, that is, on a nonempty closed subset of $\R$. At a point that is a limit from the right it is the usual derivative. At a point isolated on the right it is a difference quotient across the gap. On $\R$ it is the ordinary derivative, and on $\Z$ it is the forward difference, so it unifies differential and difference equations.