SES # | TOPICS | LECTURE NOTES |
---|---|---|

L1 | Introduction to PDEs | (PDF) |

L2 | Introduction to the heat equation | (PDF) |

L3 | The heat equation: Uniqueness | (PDF) |

L4 | The heat equation: Weak maximum principle and introduction to the fundamental solution | (PDF) |

L5 | The heat equation: Fundamental solution and the global Cauchy problem | (PDF) |

L6 | Laplace’s and Poisson’s equations | (PDF) |

L7 | Poisson’s equation: Fundamental solution | (PDF) |

L8 | Poisson’s equation: Green functions | (PDF) |

L9 | Poisson’s equation: Poisson’s formula, Harnack’s inequality, and Liouville’s theorem | (PDF) |

L10 | Introduction to the wave equation | (PDF) |

L11 | The wave equation: The method of spherical means | (PDF) |

L12 | The wave equation: Kirchhoff’s formula and Minkowskian geometry | (PDF) |

L13–L14 | The wave equation: Geometric energy estimates | (PDF) |

L15 | Classification of second order equations | (PDF) |

L16–L18 | Introduction to the Fourier transform; Fourier inversion and Plancherel’s theorem | (PDF) |

L19–L20 | Introduction to Schrödinger’s equation | (PDF) |

L21-L23 | Introduction to Lagrangian field theories | (PDF) |

L24 | Transport equations and Burger’s equation | (PDF) |

## Lecture Notes

## Course Info

##### Learning Resource Types

*assignment*Problem Sets

*grading*Exams with Solutions

*notes*Lecture Notes