Course Information
Instructor  Dr. Changhui Tan 
Lectures  M W 2:20pm  3:35pm, at LeConte 401 
Office  LeConte 422 
Office Hours  M 10:00am  12:00pm, 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 723):
 An introduction to PDEs and associated applications.
 First order linear PDE:
 Transport equation.
 Introduction to the method of characteristics.  Second order linear PDE:
 Wave equation: plane wave, traveling wave and solitons.
 Introduction to Fourier analysis.
 Laplace equation: fundamental solution, Green's function, potential theory.  Second order elliptic equations:
 Sobolev spaces, weak solutions.
 Coercivity and regularity.
Homework Assignments
 Homework assignments will be assigned and collected each week. The tentative due date is on Monday 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: 9/10, Homework 2 is available. It is due on Monday 9/16 in class.
 Download Homework Assignments.
Exams
 A final takehome exam will be given at the end of the semester. The exam will take 3 hours. You can use the textbook, your own lecture notes and your own homework assignments during the exam. Other communications and helps are not allowed. You should spend no more than 3 consecutive hours on the exam.
 Exams are under the honor code. Be sure and hand in all the work you do on each problem. Good luck!
Grades
 Your grade are distributed as below:

Class Participation » 10% Homework » 50% Final exam » 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.