Colloquium

Abstract

The notion of a "time scale" or "measure chain" wasintroduced by S. Hilger in 1988 to extend and unify discrete and continuousanalysis. Although many results from the theory of ordinary differentialequations carry over quite easily to difference equations, there are someinstances where the results for discrete equations are quite different fromtheir continuous counterparts. The introduction of a 'time scale' (which isany closed subset of the reals) permits the simultaneous treatment ofdiscrete and continuous problems. An introduction of the theory of timescales will be presented along with a discussion of some properties ofexponential functions, linear equations, and nonlinear boundary valueproblems to illustrate the applicability of the ideas.