Schedule
The class schedule below will be updated on a weekly basis. Numbers in the reading column refer to sections in the course textbook
Olver, Peter J. Introduction to Partial Differential Equations (2014) SpringerLink PDF.
Additional lecture notes will be posted in the schedule below under the "reading" column.
Lecture | Date | Topic | Reading | Notes |
1 | Sept 6 | Where do PDE come from? | Notes | Code |
2 | Sept 8 | Well-posedness. The transport equation. | 2.1,2.2 Notes | HW 1 due |
3 | Sept 13 | The wave equation: d'Alembert's formula, causality and energy methods | 2.4 Notes | |
4 | Sept 15 | Heat equation: The fundamental solution | 8.1 Notes | HW 2 due |
5 | Sept 20 | The maximum principle and energy methods | Notes | |
6 | Sept 22 | Heat and wave equations on half-lines | Notes | HW 3 due |
7 | Sept 27 | Separation of variables, Fourier Series | 3.1, 4.1 | |
8 | Sept 29 | Fourier Series | 3.2 | HW 4 due |
9 | Oct 4 | Convergence in norm | 3.5 | Code |
Oct 6 | Midterm I (in class) | |||
10 | Oct 11 | Pointwise convergence of Fourier series | 3.5 | |
11 | Oct 13 | Uniform convergence | 3.5 | HW 5 due |
12 | Oct 18 | Gibb's phenomenon | Notes | Code |
13 | Oct 20 | Separation of variables, waves and heat | 4.1 | HW 6 due |
14 | Oct 25 | Laplace and Poisson equations | 4.3 | |
15 | Oct 27 | Maximum principle and energy methods | Notes | HW 7 due |
16 | Nov 1 | Mean value formula | 4.3 | |
Nov 3 | Midterm II (in class) | |||
17 | Nov 8 | Intro to finite differences: Heat equation | 5.1,5.2 | |
18 | Nov 10 | Upwind schemes for first order equations | 5.3 | HW 8 due |
19 | Nov 15 | Finite differences for wave equation | 5.4 | |
20 | Nov 17 | Finite differences for Poisson equation | 5.5 | HW 9 due |
21 | Nov 22 | The eikonal equation and maze navigation | Notes | |
Nov 24 | Holiday (No class) | |||
22 | Nov 29 | Generalized functions | 6.1 | |
23 | Dec 1 | Generalized functions | 6.1 | HW 10 due |
24 | Dec 6 | Green's functions | 6.2 | |
25 | Dec 8 | Green's functions | 6.3 | HW 11 due |
26 | Dec 13 | Green's functions | 6.3 | |
Dec 15 | Final exam review session | HW 12 due | ||
Dec 20 | Final Exam: 4:45pm-6:45pm |