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 Lecture 15: Iterative Methods and Preconditioners Lecture 16: General Methods for Sparse Systems Lecture 17: Multigrid Methods Lecture 18: Krylov Methods / Multigrid Continued Lecture 19: Conjugate Gradient Method Lecture 20: Fast Poisson Solver Lecture 21: Optimization with constraints Lecture 22: Weighted Least Squares Lecture 23: Calculus of Variations / Weak Form Lecture 24: Error Estimates / Projections Lecture 25: Saddle Points / Inf-sup condition Lecture 26: Two Squares / Equality Constraint Bu = d Lecture 27: Regularization by Penalty Term Lecture 28: Linear Programming and Duality Lecture 29: Duality Puzzle / Inverse Problem / Integral Equations