LEC # | TOPICS | FILES |
---|---|---|

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 |

## Lecture Notes

## Course Info

##### Topics

##### Learning Resource Types

*assignment*Problem Sets

*group_work*Projects with Examples

*notes*Lecture Notes