Modeling Dynamic Systems

Abstract

Many of the physical and technological processes that are of importance in our society are difficult to describe in terms of their behavior. The cause and effect relationships are not easily discernable; there are many important variables which may play a role in the dynamic characterization of the process; the interactions between these variables may be critical. In short, many physical processes whose dynamic characterization need to be well understood are sufficiently complex that a formal approach must be followed. This formalism is best expressed in the language of mathematics. With few exceptions, our intuition, without some imposed formalism, is not capable of making sense out of the response characteristics of complex physical processes. Our objective here is to present a formal mathematical approach that is extremely useful in gaining such an understanding for a whole range of physical processes. This mathematical approach is emphasized throughout, but it is important to keep in mind that it is a tool that may be helpful in the basic task of understanding a particular physical process. Thus, the mathematical approach is by no means to be divorced from the physical process to which it is applied.