- Wednesday, February 4, 2009
- Introduction. dwarves, porridge, circulant matrix
- Friday, February 6, 2009
- ODEs, finite differences. multistep methods, Runge-Kutta, Euler, Adams
- Monday, February 9, 2009
- More finite differences, one-way wave. Lax-Friedrichs, Lax-Wendroff
- Wednesday, February 11, 2009
- Stability for one-way wave. CFL, von Neumann
- Friday, February 13, 2009
- Lax equivalence. Lax
- Tuesday, February 17, 2009
- Two-way wave, leapfrog method. wave equation, CEM
- Wednesday, February 18, 2009
- Heat equation. heat equation, Crank-Nicolson
- Friday, February 20, 2009
- Convection-diffusion. convection-diffusion
- Monday, February 23, 2009
- Black-Scholes. options, arbitrage, binomial options pricing, Black-Scholes
- Wednesday, February 25, 2009
- Conservation laws, shocks, fans. shock/fan example
- Friday, February 27, 2009
- Finite volume methods, flux limiters. Finite volume, Flux limiters
- Monday, March 2, 2009
- Level set method. Sethian's webpage, level set method, Fedkiw's animations
- Wednesday, March 4, 2009
- Linear algebra review, big and sparse matrices. condition number, sparse matrix
- Friday, March 6, 2009
- Elimination with reordering. Cholesky decomposition, minimum degree
- Monday, March 9, 2009
- Iterative methods. preconditioner, Jacobi, Gauss-Seidel, SOR
- Wednesday, March 11, 2009
- Multigrid. multigrid
- Friday, March 13, 2009
- Krylov methods. Arnoldi, Lanczos
- Monday, March 16, 2009
- Conjugate gradients. (pdf)
- Wednesday, March 18, 2009
- Fast Poisson. Poisson
- Friday, March 20, 2009
- Optimization (introduction). optimization
- Monday, March 30, 2009
- Weighted Least Squares. least squares
- Wednesday, April 1, 2009
- Calculus of Variations. action, calculus, FEM
- Friday, April 3, 2009
- Error estimates
- Monday, April 6, 2009
- Inf-sup condition
- Wednesday, April 8, 2009
- Two Squares, limit weights. lagrange multipliers
- Friday, April 10, 2009
- Regularization. Tikhonov regularization
- Monday, April 13, 2009
- Discrepancy principle
- Wednesday, April 15, 2009
- Linear programming and duality. linear programming
- Friday, April 17, 2009
- Simplex and interior point methods. simplex algorithm, Karmarkar algorithm patent
- Wednesday, April 22, 2009
- Brachistochrone with reflections. brachistochrone
- Friday, April 24, 2009
- Guest lecture: Benjamin Seibold, particle methods
- Monday, April 27, 2009
- Guest lecture: Gil Strang, SVD and circle-to-polygon
- Wednesday, April 29, 2009
- Analytic functions and complex calculus. holomorphic function, line integral, residue theorem
- Friday, May 1, 2009
- Analytic approximation, spectral method. spectral method

Project presentations