- Homework - 50%
- Midterm - 25%
- Final - 25%

Date | Topics | Supplemental Notes, Homeworks, Solutions |
---|---|---|

Aug. 22 | Introduction, Simple Harmonic Motion, Derivation of The Wave Equation | Homework 1: Exercises 1.1, 1.3, 1.10; Problem 1.1 Solutions |

Aug. 24 | d'Alembert's Formula, Separation of Variables | |

Aug. 29 | Plucked String Example, Derivation of the Heat Equation | |

Aug. 31 | Dirichlet problem on 2-D disc, Cauchy sequences | |

Sept. 5 | Fourier Series definitions, Convergences of Sequences | Homework 2: Exercise 2.6, 2.7, 2.8 Solutions |

Sept. 7 | Uniqueness of Fourier Series | |

Sept. 12 | Conditions for Uniform Convergence | |

Sept. 14 | Convolutions | |

Sept. 19 | Good Kernels | |

Sept. 21 | Abel Summability | |

Sept. 26 | Class Rescheduled | Homework 3: Exercise 2.19, 2.20 Solutions |

Sept. 28 | Vector Spaces, Hilbert Spaces | |

Oct. 3 | Mean-Square Convergence of Fourier Series | Homework 4: Exercise 3.5, 3.10; Problem 3.2 Solutions |

Oct. 5 | Mean-Square Convergence of Fourier Series Pt. 2 | |

Oct. 10 | Fall Break (Optional Review Session at 3pm) | |

Oct. 12 | Midterm | Solutions |

Oct. 17 | Heat Equation on the Ring and the Heat Kernel | |

Oct. 19 | Midterm Review and Discussion | |

Oct. 24 | The Fourier Transform Pt. 1 | Homework 5: Exercise 5.1, 5.2 Due Tuesday, Oct. 31 |

Oct. 26 | Examples, The Schroedinger Equation | |

Oct. 31 | Schwarz Space | |

Nov. 2 | Gaussians and Fourier Inversion | |

Nov. 7 | Plancherel's Formula | |

Nov. 9 | Heat Kernels Summary | |

Nov. 14 | No Class | |

Nov. 16 | The Uncertainty Principle | |

Nov. 21 | Hermite Polynomials | Homework 6: Exercise 5.23, Problem 7 Part (d) Due Tuesday, Nov. 30 |

Nov. 23 | Thanksgiving Break | |

Nov. 28 | Riemann Integration in d-Dimensions | Homework 7: Exercise 6.6, 6.9, 6.11 Hand in with your final exam |

Nov. 30 | The d-Dimensional Fourier Transform | |

Dec. 5 | The d-Dimensional Wave Equation | |

Dec. 7 | The Three-dimensional Wave Equation and Spherical Means | |

Dec. 10-13 | Final Exam | Final Exam |