- Spring 12 - Hans Lindblad

wk | date | Monday | Wednesday | Homework due following Wed. |

1 | 1/30 | InitialValueProblem | Fourier Series | 1.1,1.2,2.1,2.2 in lecture notes |

2 | 2/6 | IVP with FS, FourierTransform | FourierTransform, IVP with FT | 2.1-2,3.1-2,4.1-4 in LN |

3 | 2/13 | Weak solutions,Distributions | Operations on Distributions | 5.1-3, 6.1-6 LN |

4 | 2/20 | Fundamental Solutions | 2.2 Harmonic functions | 7.1-5 in LN, 2,3,4,6 on p 85-6 |

5 | 2/27 | 2.2.4 Green's functions. | 2.3.1 Heat equation | 8,9,11,12a,13,14 p 86-87 |

6 | 3/5 | 2.4 Wave eq. | 2.4 | 2.5: 18,19, 24 page 88-90. |

7 | 3/12 | 3.2 Characteristics | 4.6 Analytic Solutions | Evans 4,8 p 162-3, Notes 1,2 |

8 | 3/19 | break | break | |

9 | 3/26 | 5.1-2 Sobolev Spaces | 5.3 Approximation | 4,5,6 p 306 |

10 | 4/2 | 5.4 Extensions, 5.5 Traces | 5.6 Sobolev Inequalities | |

11 | 4/9 | 5.6 Sobolev Inequalities | 5.7 Compactness 5.8 PoincareIneq | 7,8,9,14,15 |

12 | 4/16 | 5.8 Difference quotients | 5.9 Other spaces | 16,17,20,21 |

13 | 4/23 | Elliptic PDE 6.1-2 Weak Sol | 6.2,App D5 Exist | |

14 | 4/30 | 6.3 Regularity | 6.5, App D 5-6 Eigenvalues | p 365-370:2,4,7,8(read 6.4),13 |