1 Fundamental concepts and examples  
2 Well-posedness and Fourier methods for linear initial value problems  
3 Laplace and Poisson equation  
4 Heat equation, transport equation, wave equation

Problem set 1 out

Project proposal due

5 General finite difference approach and Poisson equation  
6 Elliptic equations and errors, stability, Lax equivalence theorem  
7 Spectral methods

Problem set 2 out

Problem set 1 due

8 Fast Fourier transform (guest lecture by Stephen Johnson)  
9 Spectral methods  
10 Elliptic equations and linear systems  
11 Efficient methods for sparse linear systems: multigrid

Problem set 3 out

Problem set 2 due

12 Efficient methods for sparse linear systems: Krylov methods  
13 Ordinary differential equations Midterm report
14 Stability for ODE and von Neumann stability analysis  
15 Advection equation and modified equation

Problem set 4 out

Problem set 3 due

16 Advection equation and ENO/WENO  
17 Conservation laws: theory  
18 Conservation laws: numerical methods  
19 Conservation laws: high resolution methods

Problem set 5 out

Problem set 4 due

20 Operator splitting, fractional steps  
21 Systems of IVP, wave equation, leapfrog, staggered grids  
22 Level set method  
23 Navier-Stokes equation: finite difference methods  
24 Navier-Stokes equation: pseudospectral methods Problem set 5 due
25 Particle methods  
26 Project presentations Final report