New Visualization Ideas for Differential Equations

Stan Wagon
Macalester College
St. Paul, Minnesota

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Dan Schwalbe (Macalester College) and I have produced a comprehensive Mathematica package for the visualization of differential equations. We call it VisualDSolve. While most of the functions in it present solutions to DEs in familiar graphical forms, we have introduced several ideas that go beyond what has been commonly done. In this article I will discuss one such feature, the use of shaded nullcline plots to gain insight into the phase plane. Section 1 contains a discussion of an important preliminary function that is very useful in its own right: Equilibria finds all the equilibrium points in a given rectangle. Then section 2 presents the algorithm that produces shaded nullcline plots.