Illustration 1: Right-moving sin wave.
Illustration 2: Left-moving sin wave.
Illustration 3: Green's function for the heat equation, 3 shots at fixed times.
Illustration 4: Green's function for the heat equation, animation.
Illustration 5: The Airy function Ai(x).
Illustration 6: Green's function for a third order linear dispersive PDE.
Illustration 7: Blow up in a simple nonlinear equation.