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