OVERVIEW

Ask any engineer who is more than one year (one month?) out of college if he or she ever uses calculus on the job, and the answer will probably be "Never!" Ask that same engineer if he or she could still work a calculus (or differential equations) problem, and the response will likely be a horrified stare, followed by "Are you kidding?"

It is all too true that many engineers regard their math courses only as a necessary evil required to obtain their degree, but never to be used thereafter. "After all, I work in the real world!" they say. This negative notion of mathematics probably stems from their memory of late nights spent working tedious homework problems as well as their (or their professors ) failure to associate the concepts of mathematics to the real world. It also may relate to the fact that these engineering students' subsequent success on the job probably does not depend upon their ability to produce an analytical solution to a calculus problem or a differential equation.

Outside the realm of the professional mathematician, the need to actually be able to solve a differential equation, on paper, has been all but eliminated by the availability of computer-generated solutions. Yet, in many engineering disciplines, the ability to conceptualize a problem in mathematical terms is still an invaluable asset. That ability is what distinguishes the engineer from the technician.

Nowhere is this truer than in the field of process control. Here we are concerned with dynamic...