Editing Time-scale calculus (section)

{{short description|Unification of discrete and continuous theories of calculus}}

In [[mathematics]], '''time-scale calculus''' is a unification of the theory of [[difference equation]]s with that of [[differential equation]]s, unifying [[integral]] and [[differential calculus]] with the [[calculus of finite differences]], offering a formalism for studying [[hybrid system]]s.  It has applications in any field that requires simultaneous modelling of [[Discrete time and continuous time|discrete and continuous]] data. It gives a new definition of a [[derivative]] such that if one differentiates a function defined on the [[real number]]s then the definition is equivalent to standard differentiation, but if one uses a function defined on the [[integer]]s then it is equivalent to the [[forward difference]] operator.