Notes

For the sake of plotting and simple mathematical manipulations, I will occasionally use Maple.
You are not required to learn or use Maple; you can use anything you want to make plots
(including doing them by hand). For those who do want to use Maple, more information and
a tutorial are available here

Here is the Maple file illustrating the solution to  u_x+u_y+cu=0 with c=1, u(x,0)=exp(-x²/2).

Here is the Maple for (1+u)ux+uy=0,  u(x,0)=exp(-x²/2).

Here is the Maple for the shock formation and propagation example.

Here is the Maple for the sand pile on an ellipse.

Here is the Maple for the second order, linear, const coefficient  PDE example

Maple for the nonconstant coefficient 2nd order PDE example

Maple for the linear wave equation.

Maple for the forced wave equation.

Halfline wave equation: u(0,y)=0.  u_x(0,y)=0

Modal solution to the wave propagation problem on a finite interval

Modal coefficients for various initial conditions

IVPs for the heat equation