## Schedule

The class schedule below will be updated on a weekly basis. Numbers in the reading column refer to sections in the course textbook

Olver, Peter J.

**Introduction to Partial Differential Equations**(2014) SpringerLink PDF.Additional lecture notes will be posted in the schedule below under the "reading" column.

Lecture |
Date |
Topic |
Reading |
Notes |

1 | Sept 6 | Where do PDE come from? | Notes | Code |

2 | Sept 8 | Well-posedness. The transport equation. | 2.1,2.2 Notes | HW 1 due |

3 | Sept 13 | The wave equation: d'Alembert's formula, causality and energy methods | 2.4 Notes | |

4 | Sept 15 | Heat equation: The fundamental solution | 8.1 Notes | HW 2 due |

5 | Sept 20 | The maximum principle and energy methods | Notes | |

6 | Sept 22 | Heat and wave equations on half-lines | Notes | HW 3 due |

7 | Sept 27 | Separation of variables, Fourier Series | 3.1, 4.1 | |

8 | Sept 29 | Fourier Series | 3.2 | HW 4 due |

9 | Oct 4 | Convergence in norm | 3.5 | Code |

Oct 6 | Midterm I (in class) |
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10 | Oct 11 | Pointwise convergence of Fourier series | 3.5 | |

11 | Oct 13 | Uniform convergence | 3.5 | HW 5 due |

12 | Oct 18 | Gibb's phenomenon | Notes | Code |

13 | Oct 20 | Separation of variables, waves and heat | 4.1 | HW 6 due |

14 | Oct 25 | Laplace and Poisson equations | 4.3 | |

15 | Oct 27 | Maximum principle and energy methods | Notes | HW 7 due |

16 | Nov 1 | Mean value formula | 4.3 | |

Nov 3 | Midterm II (in class) |
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17 | Nov 8 | Intro to finite differences: Heat equation | 5.1,5.2 | |

18 | Nov 10 | Upwind schemes for first order equations | 5.3 | HW 8 due |

19 | Nov 15 | Finite differences for wave equation | 5.4 | |

20 | Nov 17 | Finite differences for Poisson equation | 5.5 | HW 9 due |

21 | Nov 22 | The eikonal equation and maze navigation | Notes | |

Nov 24 | Holiday (No class) |
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22 | Nov 29 | Generalized functions | 6.1 | |

23 | Dec 1 | Generalized functions | 6.1 | HW 10 due |

24 | Dec 6 | Green's functions | 6.2 | |

25 | Dec 8 | Green's functions | 6.3 | HW 11 due |

26 | Dec 13 | Green's functions | 6.3 | |

Dec 15 | Final exam review session | HW 12 due | ||

Dec 20 |
Final Exam: 4:45pm-6:45pm |