| 1 | Fundamental concepts and examples | (PDF) |
| 2 | Well-posedness and Fourier methods for linear initial value problems | (PDF) |
| 3 | Laplace and Poisson equation | (PDF) |
| 4 | Heat equation, transport equation, wave equation | (PDF) |
| 5 | General finite difference approach and Poisson equation | (PDF) |
| 6 | Elliptic equations and errors, stability, Lax equivalence theorem | (PDF) |
| 7 | Spectral methods | (PDF) |
| 8 |
Fast Fourier transform (guest lecture by Steven Johnson) | |
| 9 | Spectral methods | (PDF) |
| 10 | Elliptic equations and linear systems | (PDF) |
| 11 | Efficient methods for sparse linear systems: Multigrid | (PDF) |
| 12 | Efficient methods for sparse linear systems: Krylov methods | (PDF) |
| 13 | Ordinary differential equations | (PDF) |
| 14 | Stability for ODE and von Neumann stability analysis | (PDF) |
| 15 | Advection equation and modified equation | (PDF) |
| 16 | Advection equation and ENO/WENO | (PDF) |
| 17 | Conservation laws: Theory | (PDF) |
| 18 | Conservation laws: Numerical methods | (PDF) |
| 19 | Conservation laws: High resolution methods | (PDF) |
| 20 | Operator splitting, fractional steps | (PDF) |
| 21 | Systems of IVP, wave equation, leapfrog, staggered grids | (PDF) |
| 22 | Level set method | (PDF) |
| 23 | Navier-Stokes equation: Finite difference methods | (PDF) |
| 24 | Navier-Stokes equation: Pseudospectral methods | (PDF) |
| 25 | Particle methods | (PDF) |
| 26 | Project presentations | |
