L1 | Introduction to PDEs | |

L2 | Introduction to the heat equation | |

L3 | The heat equation: Uniqueness | Problem Set 1 due |

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

L5 | The heat equation: Fundamental solution and the global Cauchy problem | Problem Set 2 due |

L6 | Laplace's and Poisson's equations | |

L7 | Poisson's equation: Fundamental solution | Problem Set 3 due |

L8 | Poisson's equation: Green functions | |

L9 | Poisson's equation: Poisson's formula, Harnack's inequality, and Liouville's theorem | Problem Set 4 due |

L10 | Introduction to the wave equation | Problem Set 5 due |

L11 | The wave equation: The method of spherical means | |

L12 | The wave equation: Kirchhoff's formula and Minkowskian geometry | Problem Set 6 due |

L13 | The wave equation: Geometric energy estimates | |

E1 | Midterm Exam | |

L14 | The wave equation: Geometric energy estimates (cont.) | |

L15 | Classification of second order equations | Problem Set 7 due |

L16 | Introduction to the Fourier transform | |

L17 | Introduction to the Fourier transform (cont.) | Problem Set 8 due |

L18 | Fourier inversion and Plancherel's theorem | |

L19 | Introduction to Schrödinger's equation | Problem Set 9 due |

L20 | Introduction to Schrödinger's equation (cont.) | |

L21 | Introduction to Lagrangian field theories | Optional (Bonus) Problem due |

L22 | Introduction to Lagrangian field theories (cont.) | Problem Set 10 due |

L23 | Introduction to Lagrangian field theories (cont.) | |

L24 | Transport equations and Burger's equation | Problem Set 11 due |

E2 | Final Exam | |