TABLE OF CONTENTS The need to study various mathematical techniques grows out of the requirement to understand, solve and/or evaluate the different types of equations that arise from the mathematical modeling of phenomena in the natural, social, and engineering sciences. The first equations written down for a particular system involve a number of parameters appearing in the equations relating variable quantities. What is generally required, at this point, is to convert these equations into structurally similar equations, but having the important property that all of the new parameters and variables have no physical dimensions. One of the purposes of this chapter is to provide some indication as to how to do this and illustrate the basic method by means of examples.
The final section briefly introduces the concept of nonlinearity and the important role that it plays in the sciences. The bibliography gives a short listing of books and related materials on the main issues raised in this chapter.
Suppose there is a system that you want to understand. This understanding may include the correlation of its past behavior with the current state of the system, along with the ability to predict its future evolution. An important tool for obtaining such information is to construct a mathematical model for the relevant phenomena related to the system. The particular mathematical formalism used will depend on the nature of the system. It should be pointed out that the same system can have various mathematical representations with the one selected dependent upon what...
