Infinitesimal Time Scale Calculus

The theory of calculus was first done via the use of "infinitesimal quantities" which had no rigorous foundation. Mathematicians corrected this lack of rigor by introducing the notion of a limit, and they were able to rewrite all of differential calculus in terms of these limits. In the 1960's, Abraham Robinson constructed a field called the hyperreals that has the same properties of the infinitesimals with a firm foundation. This construction led to the study of infinitesimal calculus over hyperreals. This talk will present the basics of hyperreal numbers and the basic theorems of time scale calculus by considering the hyperreal extensions of traditional time scales.