Editing Time-scale calculus (section)

==Dynamic equations==
Many results concerning differential equations carry over quite easily to corresponding results for difference equations, while other results seem to be completely different from their [[continuous function|continuous]] counterparts.<ref name=bp>{{cite book | author=Martin Bohner & Allan Peterson | title=Dynamic Equations on Time Scales | publisher=Birkhäuser | year=2001 | isbn=978-0-8176-4225-9 }}</ref>  The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice—once for differential equations and once again for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown [[function (mathematics)|function]] is a so-called time scale (also known as a time-set), which may be an arbitrary closed subset of the reals. In this way, results apply not only to the [[Set (mathematics)|set]] of [[real number]]s or set of [[integer]]s but to more general time scales such as a [[Cantor set]].

The three most popular examples of [[calculus]] on time scales are [[differential calculus]], [[finite differences|difference calculus]], and [[quantum calculus]]. Dynamic equations on a time scale have a potential for applications such as in [[population dynamics]]. For example, they can model insect populations that evolve continuously while in season, die out in winter while their eggs are incubating or dormant, and then hatch in a new season, giving rise to a non-overlapping population.