1st-Difference Methods for Ordinary Differential Equations

2-Finite Differences, Accuracy, Stability, Convergence

3-The One-way Wave Equation and CFL / von Neumann Stability

4-Comparison of Methods for the Wave Equation

5-Second-order Wave Equation (including leapfrog)

6-Wave Profiles, Heat Equation / point source

7-Finite Differences for the Heat Equation

8-Convection-Diffusion / Conservation Laws

9-Conservation Laws / Analysis / Shocks

10-Shocks and Fans from Point Source

11-Level Set Method

12-Matrices in Difference Equations (1D, 2D, 3D)

13-Elimination with Reordering: Sparse Matrices

14-Financial Mathematics / Black-Scholes Equation

15-Iterative Methods and Preconditioners

16-General Methods for Sparse Systems

17-Multigrid Methods

18-Krylov Methods / Multigrid Continued

19-Conjugate Gradient Method

20-Fast Poisson Solver

21-Optimization with constraints

22-Weighted Least Squares

23-Calculus of Variations / Weak Form

24-Error Estimates / Projections

25-Saddle Points / Inf-sup condition

26-Two Squares / Equality Constraint Bu = d

27-Regularization by Penalty Term

28-Linear Programming and Duality

29-Duality Puzzle / Inverse Problem / Integral Equations