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.
Lectures on the calculus of variations will be based on my lecture notes
Calder, Jeff. The Calculus of Variations [pdf]. (Updated Jan 19)
These notes also contain background mathematical material that may be useful to review. Keep in mind these notes will be updated frequently throughout the first few weeks of the course.
| Lecture | Date | Topic | Reading | Notes |
| 1 | Jan 17 | Calculus of variations | Notes | |
| 2 | Jan 19 | Calculus of variations | Notes | HW 1 due |
| 3 | Jan 24 | Calculus of variations | Notes | |
| 4 | Jan 26 | Calculus of variations | Notes | HW 2 due |
| 5 | Jan 31 | Calculus of variations | Notes | Code |
| 6 | Feb 2 | Calculus of variations | Notes | HW 3 due |
| 7 | Feb 7 | Calculus of variations | Notes | |
| 8 | Feb 9 | Fourier Transform (Notes) | 7.1 | HW 4 due |
| 9 | Feb 14 | Fourier Transform (Notes) | 7.2 | |
| Feb 16 | Midterm I (in class) | |||
| 10 | Feb 21 | Fourier Transform (Notes) | 7.3,8.1 | |
| 11 | Feb 23 | Fourier Transform | 8.3 | HW 5 due |
| 12 | Feb 28 | Maximum Principle (Notes) | 8.3 | |
| 13 | Mar 2 | Maximum Principle | 8.3 | HW 6 due |
| 14 | Mar 7 | Maximum Principle (Notes) | ||
| 15 | Mar 9 | Viscosity solutions (Notes) | HW 7 due | |
| Mar 14 | Spring Break (No class) | |||
| Mar 16 | Spring Break (No class) | |||
| 16 | Mar 21 | The wave equation (Notes) | 12.6 | |
| 17 | Mar 23 | The wave equation (Notes) | 12.6 | HW 8 due |
| 18 | Mar 28 | The Finite Element Method | 10.1-10.4 | |
| Mar 30 | Midterm II (in class) | |||
| 19 | Apr 4 | The Finite Element Method (Notes) | 10.1-10.4 | |
| 20 | Apr 6 | Scalar conservation laws (Notes) | 2.3 | HW 9 due |
| 21 | Apr 11 | Scalar conservation laws (Notes) | 2.3 | |
| 22 | Apr 13 | Hamilton-Jacobi equations (Notes) | HW 10 due | |
| 23 | Apr 18 | Hamilton-Jacobi equations (Notes,Extra) | ||
| 24 | Apr 20 | Hamilton-Jacobi equations | HW 11 due | |
| 25 | Apr 25 | Optimal control theory (Notes) | ||
| 26 | Apr 27 | Hopf-Lax and Differential games (Notes) | ||
| 27 | May 2 | Differential games (Notes) | HW 12 due | |
| May 4 | Final exam review session | |||
| May 9 | Final Exam: Vincent 206, 4:45pm-6:45pm |