Course Information
Instructor  Dr. Changhui Tan 
Lectures  T Th 11:40am  12:55pm, at LeConte 121 
Office  LeConte 422 
Office Hours  T Th 10:00am  11:00pm, or by appointment 
Textbooks  Lawrence C. Evans, Partial Differential Equations. (ISBN: 9780821849743) 
Course Description
 The official course description for the MATH 723/724 sequence:
 Elliptic equations: fundamental solutions, maximum principles, Green’s function, energy method and Dirichlet principle; Sobolev spaces: weak derivatives, extension and trace theorems; weak solutions and Fredholm alternative, regularity, eigenvalues and eigenfunctions.
 Detailed study of the following topics: method of characteristics; HamiltonJacobi equations; conservation laws; heat equation; wave equation; linear parabolic equations; linear hyperbolic equations.
 List of Topics (for MATH 724):
 Second order linear PDE:
 Heat equation: diffusion, mean value theorem, maximum principle.  Second order parabolic equations:
 Weak solutions.
 Strong solutions and regularity theory.
 Mild solutions and semigroup theory.
 Topic: Incompressible NavierStokes equations.  Hyperbolic conservation laws:
 Weak solutions, entropy solutions, existence and uniqueness theory.
 Riemann problem, shock and rarefaction waves.
 System of conservation laws. Riemann invariants.
 Topic: Compressible Euler and related systems. [* if time permits]
 Second order linear PDE:
Online Lectures
 Due to the coronavirus pandemic, online lectures will be offered starting from March 24th, via Blackboard Collaborate Ultra. You can access the virtual classroom from the course page at Blackboard (Click "Online Lectures") at normal lecture time. A webcam and microphone is needed for communication. Alternatively, you can join as a guest through the direct link HERE. Lectures will be recorded for future access.
 Office hours will also be offered via internet. A session has been created in the Blackboard system. Click HERE for a direct guest access. Other than the regular office hours, appointment can be made via email.
 Download Notes for Online Lectures.
Homework Assignments
 Homework assignments will be assigned and collected each week. The tentative due date is on Tuesday in class.
 The homework is not pledged. You are encouraged to discuss the problems. However, each student is responsible for the final preparation of his/her own homework papers.
 Last update: 4/9, homework 6 is available. It is due on Tuesday 4/21 by the end of the day. Problem 3 in homework 5 has been moved to homework 6.
 Download Homework Assignments.
Project
 There will be a final project. This is a group work. There is no restrictions on what should be done. You are encouraged to propose questions, apply what we have learned in class, search for literatures, discuss in groups, and consult with the instructor. The outcome should be presented in a report (for each group), typed in LaTex, as well as a 45 minutes to 1 hour presentation on the exam day April 30 12:303:00pm.
 Last update: 4/22, instructions for the project presentation is available.
 Download the Projects. Instructions for the final presentation.
Grades
 Your grade are distributed as below:

Class Participation » 10% Homework » 50% Project » 40%
Contact Information
 Contact me at This email address is being protected from spambots. You need JavaScript enabled to view it. if you have any questions.