I will put copies of the Mathematica worksheets I prepare for class here.
Explicit finite diff. This worksheet illustrates the simple, explicit finite difference approximation for solutions of the heat equation.
Implicit finite diff. This worksheet illustrates the simple, implicit finite difference approximation for solutions of the heat equation. In particular, one sees that it has much better stability properties than the explicit scheme.
Crank-Nicholson This worksheet illustrates the Crank-Nicholson finite difference approximation for solutions of the heat equation.
Wave Equation This notebook computes a finite difference approximation to solutions of the wave equation and then animates the results. Characteristic Method This notebook computes a solution to a transport equation with non-constant coefficients with the method of characteristics. Rayleigh-Ritz Method This notebook uses the Rayleigh-Ritz method to approximate the eigenvalues of the second derivative operator with Dirichlet boundary conditions. Finite Element Method This notebook illustrates the finite element method.