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: 978-0821849743) |
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; Hamilton-Jacobi 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: 11/6, Homework 8 is available. It is due on Monday 11/11 in class.
Download Homework Assignments.
Exams
- A final take-home 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!
- Last update: 12/6, the final exam is available.
Download the Final Exam.
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.