Schedule


The class schedule below will be updated on a weekly basis. Numbers in the reading column refer to sections in the course textbook

Evans, L.C. (2010). Partial Differential Equations, 2nd Edition, AMS.

Lecture Date Topic Reading Notes
1 Aug 26 Derivation of fundamental PDE I
2 Aug 28 Derivation of fundamental PDE II 2.1
3 Aug 31 Laplace's equation 2.2
4 Sept 2 Mean value property and maximum principle 2.2
5 Sept 4 Derivative estimates and inequalities 2.2 HW 1 due
Sept 7 Holiday (No class)
6 Sept 9 Green's functions I 2.2
7 Sept 11 Green's functions II 2.2
8 Sept 14 The Fourier Transform 4.3
9 Sept 16 Heat equation and Bessel Potentials 4.3,2.3
10 Sept 18 Mean value formula for heat equation 2.3 HW 2 due
11 Sept 21 Maximum principle and regularity for heat equation 2.3
12 Sept 23 Energy methods and backwards uniqueness 2.3
13 Sept 25 The 1D wave equation: d'Alembert's formula 2.3
14 Sept 28 The wave equation in 3D and then 2D 2.3
15 Sept 30 Energy methods for the wave equation 2.3 HW 3 due
16 Oct 2 Method of characteristics: Introduction 3.2
17 Oct 5 Method of characteristics: Local uniqueness 3.2
18 Oct 7 Calculus of Variations 3.3 HW 4 due
19 Oct 9 Hamilton-Jacobi Equations 3.3
20 Oct 12 Hopf-Lax Formula 3.3 MT due
21 Oct 14 Scalar conservation laws 3.4
22 Oct 16 Lax-Oleinik formula 3.4
23 Oct 19 Lax-Oleinik formula and entropy solutions 3.4
24 Oct 21 Uniqueness of entropy solutions 3.4
25 Oct 23 Separation of variables 4.1 HW 5 due
26 Oct 26 Turing instability 4.1
27 Oct 28 Sobolev spaces 5.1,5.2
28 Oct 30 Completeness 5.2
29 Nov 2 Approximation by smooth functions 5.3
30 Nov 4 Extensions 5.4 HW 6 due
31 Nov 6 Trace operator 5.5
32 Nov 9 Sobolev Inequalities 5.6
Nov 11 Holiday (No class)
33 Nov 13 Sobolev inequalities 5.6
34 Nov 16 Sobolev inequalities 5.6 HW 7 due
35 Nov 18 Compactness 5.7
36 Nov 20 Poincare inequalities 5.8
37 Nov 23 Elliptic equations: Weak solutions and Lax-Milgram 6.2 HW 8 due
Nov 25 Holiday (No class)
Nov 27 Holiday (No class)
38 Nov 30 Elliptic equations: Energy estimates and existence 6.2
39 Dec 2 Elliptic equations: Fredholm alternative 6.2
40 Dec 4 Elliptic equations 6.2
Dec 11 Final Exam Starts HW 9 due
Dec 14 Final Exam Due