Lecture Details

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