New Visualization Ideas for Differential Equations
Stan Wagon
Macalester College
St. Paul, Minnesota
Abstract:

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.