Algebraic Models

Abstract

Computer algebra or symbolic computation systems such as Maple have the ability to manipulate mathematical structures in a symbolic or algebraic manner in contrast to conventional mathematical programs which require numerical values for all variables. In this chapter we, your computational science “chefs,” introduce the reader to the the first level of symbolic computation recipes in our Maple computer menu. These recipes consist of an intellectually stimulating sample of scalar and vector algebraic models that scientists and engineers are likely to encounter early in their undergraduate training. The computer algebra system is used to symbolically derive, manipulate, and solve a wide variety of simple, yet interesting, scientific model equations. In the symbolic computation sections of this text, the models are grouped according to the type of mathematical formulation, starting with the easiest, namely algebraic models in this chapter, followed by models based on ordinary differential equations (ODEs) in Chapters 6 and 7, difference equation models in Chapter 8, and partial differential equation (PDE) models in Chapter 12. The emphasis is on not stressing the reader, but instead gently introducing you to Maple’s symbohc manipulation capability. So, keep this in mind when reading the first few topics in this chapter where the inteUigent reader could readily do many parts of the calculations by hand. As you progress through The Entrees, however, the examples will become more involved and either difficult or impossible to solve with pen and paper. In any case, we trust that you will enjoy the topics of this chapter as well as the recipes that will be served later.