One of the fundamental problems in many areas of science and engineering is the problem of modeling and simulation. Scilab provides a large array of tools for developing and simulating models of several types. For several of these tools it is possible to use them with abbreviated commands and default values of some parameters. However, to know how to choose the appropriate tools and how to get the kind of answers desired, it is often necessary to know something about how the algorithms are set up and what to do if there are difficulties.
In this chapter we shall describe the types of models that are available in Scilab and some of the tools available for their simulation. We shall also give some general comments about how to use the tools and how to choose between the tools.
One of the most popular types of model is that of ordinary differential equations (ODE) such as
Here y and f may be vector valued, y is a function of the real variable t, and 
denotes the derivative of y with respect to t. System (3.1) is a first-order equation since it involves only first-order derivatives.
Some models are initially formulated in terms of higher derivatives, but they can always be rewritten as first-order systems by the introduction of additional variables. The Scilab tools assume that the differential equation has first been rewritten to be of first...
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