If one permits solutions to have discontinuous derivatives, as is the case in the next section, then additional solutions are possible. If you cover differential inclusions, you may wish to have the students find some of these other solutions. Differential inclusions are tacitly covered when topics on nonlinear differential equations are covered. The requirement that the derivative of a solution be continuous affords little opportunity to mention how to resolve multiple choices for the value of a derivative. This chapter requires few supporting notebooks.
Notebooks become important in the next chapter.
There is one package for use in this chapter, SolveNonlinearDE.m . Others can get all of the necessary files by anonymous ftp from cross.sewanee.edu . Use your e-mail address as the password. This notebook contains the code for Stan Wagon's direction field drawing function, SlopeLines , along with an example of how to use SlopeLines . The techniques appearing here are likely to occur often as you illustrate ideas for your class.