Schedule
The class schedule below will be updated on a weekly basis. Numbers in the reading column refer to sections in the course textbook
Strauss, Walter A. (2007). Partial Differential Equations: An Introduction, 2nd Edition, Wiley.
| Lecture | Date | Topic | Reading | Notes |
| 1 | Aug 26 | Where do PDE come from? | 1.2,1.3 | |
| 2 | Aug 28 | Initial/boundary conditions and well-posedness | 1.1,1.4,1.5 | |
| 3 | Aug 31 | The wave equation, causality and energy | 2.1,2.2 | |
| 4 | Sept 2 | The diffusion equation: Maximum principle | 2.3 | |
| 5 | Sept 4 | Diffusion on the whole line | 2.4 | HW 1 due |
| Sept 7 | Holiday (No class) | |||
| 6 | Sept 9 | Differences between waves and diffusion | 2.5 | |
| 7 | Sept 11 | Heat eqation on the half-line | 3.1 | HW 2 due |
| 8 | Sept 14 | Separation of variables for heat flow: Fourier series | 4.1,4.2 | |
| 9 | Sept 16 | Fourier series | 5.1-5.3 | |
| 10 | Sept 18 | Differentiating under an integral | ||
| 11 | Sept 21 | L2 convergence of Fourier series | 5.4 | HW 3 due |
| 12 | Sept 23 | Pointwise convergence of Fourier series | 5.5 | |
| 13 | Sept 25 | Discontinuous functions and uniform convergence | 5.5 | HW 4 due |
| 14 | Sept 28 | Gibb's Phenomenon | ||
| 15 | Sept 30 | Regularity and decay of Fourier coefficients | ||
| 16 | Oct 2 | Solving PDE with Fourier series | HW 5 due | |
| 17 | Oct 5 | Laplace's equation | 6.1 | |
| 18 | Oct 7 | Harmonic funtions | 6.1 | |
| Oct 9 | Midterm | |||
| 19 | Oct 12 | Poisson's formula | 6.3 | |
| 20 | Oct 14 | Laplace's equation in wedges and annuli | 6.4 | |
| 21 | Oct 16 | Green's identities | 7.1, 7.2 | HW 6 due |
| 22 | Oct 19 | Dirichlet's principle | 7.1, 7.2 | |
| 23 | Oct 21 | Green's functions | 7.3 | |
| 24 | Oct 23 | Green's functions | 7.3 | HW 7 due |
| 25 | Oct 26 | Finite difference schemes | 8.1, 8.2 | |
| 26 | Oct 28 | Rate of convergence for heat equation | ||
| 27 | Oct 30 | Finite differences for wave equation | 8.3 | HW 8 due |
| 28 | Nov 2 | Finite differences for Laplace's equation | 8.4 | |
| 29 | Nov 4 | Convergence of Jacobi iterations | ||
| 30 | Nov 6 | Wave equation in 3D | 9.1, 9.2 | HW 9 due |
| 31 | Nov 9 | Wave equation in 2D | 9.2 | |
| Nov 11 | Holiday (No class) | |||
| 32 | Nov 13 | Distributions | 12.1 | |
| 33 | Nov 16 | Distributions | 12.2 | HW 10 due |
| 34 | Nov 18 | Fourier transform | 12.3 | |
| 35 | Nov 20 | Fourier transform | 12.4 | |
| 36 | Nov 23 | Fourier transform | 12.4 | HW 11 due |
| Nov 25 | Holiday (No class) | |||
| Nov 27 | Holiday (No class) | |||
| 37 | Nov 30 | Scalar conservation laws | 14.1 | |
| 38 | Dec 2 | Scalar conservation laws | 14.1 | |
| 39 | Dec 4 | Scalar conservation laws | 14.1 | |
| Dec 11 | Final exam review session | HW 12 due | ||
| Dec 14 | Final Exam: 7pm-10pm |