MATH 7530 - Fall 2024

Below is a course schedule. It contains an outline of course topics, homework, quiz and exam dates.

Note: This schedule is approximate and will evolve as the course progresses. Lectures may be rearranged and split between days depending on course progress. The exams dates are tentative and will be finalized at least a couple weeks before the date.

Week	Date	Topics	Section	HW
1	Introduction and Laplace/Elliptic Equations		Ch1,2.2
	M 8/19	Introduction	1.1, 1.2, 1.3
	W 8/21	Transport Equations $u_t + b\cdot\nabla u=0$, Laplace's Equations $\Delta u = 0$	2.1,2.2
	F 8/23	Poisson's Equation $\Delta u = f$	2.2
2	M 8/26	Harmonic Functions, Mean Value Formula and Maximum Principle	2.2
	W 8/28	Smoothness of Solutions, Liouville's Theorem	2.2
	F 8/30	Regularity Estimates	2.2
3	M 9/2	Labor Day - No Class
	W 9/4	Analyticity	2.2
	F 9/6	Harnack's Inequality, Green's functions	2.2	Problem Set 1 Due
4	M 9/9	Green's functions and BVPs	2.2
	W 9/11	Class Cancelled
	F 9/13	Poisson's Formula	2.2
5	M 9/16	Energy Methods	2.2
	Heat/Parabolic Equations		Ch2
	W 9/18	Heat Equation $u_t - \Delta u = 0$ and heat Kernel	2.3
	F 9/20	IVP, Duhamels principle	2.3	Problem Set 2 Due
6	M 9/23	Mean value formula	2.3
	W 9/25	Maximum principle and uniqueness	2.3
	F 9/27	Regularity	2.3
7	M 9/30	Energy methods and backwards uniqueness	2.3
	Wave Equation and Sobolev Spaces		Ch2
	W 10/2	Wave Equation		Problem Set 3 Due
	F 10/4	Fall Break - No Class
8	Nonlinear first Order PDE		Ch4
	M 10/7	Complete integrals and Envelopes
	W 10/9
	F 10/11
9	M 10/14
	W 10/16
	F 10/18
10	M 10/21
	W 10/23
	F 10/25
11	M 10/28
	W 10/30			Take Home Exam 1 Due
	F 11/1
12	M 11/4
	W 11/6
	F 11/8
13	M 11/11
	W 11/13
	F 11/15
14	M 11/18
	W 11/20
	F 11/22
15	M 11/25	Thanksgiving Break - No Class
	W 11/27	Thanksgiving Break - No Class
	F 11/29	Thanksgiving Break - No Class
16	M 12/2
	W 12/4
	F 12/6
17	W 12/11	Exam

Course Schedule

MATH 7530 - Fall 2024