“Modeling” is the process of developing sets of equations and formulas describing some process of interest. This process may be the falling of a frozen duck, the changes in a population over time, the consumption of fuel by a car traveling various distances, the electronic transmission of information, or any of a huge number of other processes. A major goal of modeling is to predict “how things will turn out” at some point of interest, be it a point of time in the future or a position along the road. Along with this, is often a desire to use the model to determine changes that can be made to the process to force things to turn out as desired.
This chapter examines various aspects of modeling using first-order differential equations. This is done by looking at illustrative examples, interspersed with more general discussions on how to go about developing and using models with first-order equations. These discussions concern the choosing of appropriate variables, determining how complete or simple the model should be, and testing the model.