Lecture Notes

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