### Lessons

- Lecture 1: Difference Methods for Ordinary Differential Equations
- Lecture 2: Finite Differences, Accuracy, Stability, Convergence
- Lecture 3: The One-way Wave Equation and CFL / von Neumann Stability
- Lecture 4: Comparison of Methods for the Wave Equation
- Lecture 5: Second-order Wave Equation (including leapfrog)
- Lecture 6: Wave Profiles, Heat Equation / point source
- Lecture 7: Finite Differences for the Heat Equation
- Lecture 8: Convection-Diffusion / Conservation Laws
- Lecture 9: Conservation Laws / Analysis / Shocks
- Lecture 10: Shocks and Fans from Point Source
- Lecture 11: Level Set Method
- Lecture 12: Matrices in Difference Equations (1D, 2D, 3D)
- Lecture 13: Elimination with Reordering: Sparse Matrices
- Lecture 14: Financial Mathematics / Black-Scholes Equation