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 | |