## Schedule

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

Evans, L.C. (2010).

**Partial Differential Equations**, 2nd Edition, AMS.Lecture |
Date |
Topic |
Reading |
Notes |

1 | Aug 26 | Derivation of fundamental PDE I | ||

2 | Aug 28 | Derivation of fundamental PDE II | 2.1 | |

3 | Aug 31 | Laplace's equation | 2.2 | |

4 | Sept 2 | Mean value property and maximum principle | 2.2 | |

5 | Sept 4 | Derivative estimates and inequalities | 2.2 | HW 1 due |

Sept 7 | Holiday (No class) |
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6 | Sept 9 | Green's functions I | 2.2 | |

7 | Sept 11 | Green's functions II | 2.2 | |

8 | Sept 14 | The Fourier Transform | 4.3 | |

9 | Sept 16 | Heat equation and Bessel Potentials | 4.3,2.3 | |

10 | Sept 18 | Mean value formula for heat equation | 2.3 | HW 2 due |

11 | Sept 21 | Maximum principle and regularity for heat equation | 2.3 | |

12 | Sept 23 | Energy methods and backwards uniqueness | 2.3 | |

13 | Sept 25 | The 1D wave equation: d'Alembert's formula | 2.3 | |

14 | Sept 28 | The wave equation in 3D and then 2D | 2.3 | |

15 | Sept 30 | Energy methods for the wave equation | 2.3 | HW 3 due |

16 | Oct 2 | Method of characteristics: Introduction | 3.2 | |

17 | Oct 5 | Method of characteristics: Local uniqueness | 3.2 | |

18 | Oct 7 | Calculus of Variations | 3.3 | HW 4 due |

19 | Oct 9 | Hamilton-Jacobi Equations | 3.3 | |

20 | Oct 12 | Hopf-Lax Formula | 3.3 | MT due |

21 | Oct 14 | Scalar conservation laws | 3.4 | |

22 | Oct 16 | Lax-Oleinik formula | 3.4 | |

23 | Oct 19 | Lax-Oleinik formula and entropy solutions | 3.4 | |

24 | Oct 21 | Uniqueness of entropy solutions | 3.4 | |

25 | Oct 23 | Separation of variables | 4.1 | HW 5 due |

26 | Oct 26 | Turing instability | 4.1 | |

27 | Oct 28 | Sobolev spaces | 5.1,5.2 | |

28 | Oct 30 | Completeness | 5.2 | |

29 | Nov 2 | Approximation by smooth functions | 5.3 | |

30 | Nov 4 | Extensions | 5.4 | HW 6 due |

31 | Nov 6 | Trace operator | 5.5 | |

32 | Nov 9 | Sobolev Inequalities | 5.6 | |

Nov 11 | Holiday (No class) |
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33 | Nov 13 | Sobolev inequalities | 5.6 | |

34 | Nov 16 | Sobolev inequalities | 5.6 | HW 7 due |

35 | Nov 18 | Compactness | 5.7 | |

36 | Nov 20 | Poincare inequalities | 5.8 | |

37 | Nov 23 | Elliptic equations: Weak solutions and Lax-Milgram | 6.2 | HW 8 due |

Nov 25 | Holiday (No class) |
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Nov 27 | Holiday (No class) |
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38 | Nov 30 | Elliptic equations: Energy estimates and existence | 6.2 | |

39 | Dec 2 | Elliptic equations: Fredholm alternative | 6.2 | |

40 | Dec 4 | Elliptic equations | 6.2 | |

Dec 11 |
Final Exam Starts |
HW 9 due | ||

Dec 14 |
Final Exam Due |