Video Lectures

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