Course Information
| Instructor | Dr. Changhui Tan |
| Lectures | Tu Th 9:25am - 10:40am, at HBH 227 |
| Office | HBH 426 |
| Office Hours | Th 11:00am - 12:00pm, or by appointment |
| Teaching Assistants | Chao Li |
| TA Office Hours | M 2:30pm - 3:30pm, at HBH 36 |
| Textbooks | Lawrence C. Evans, Partial Differential Equations. (ISBN: 978-0821849743) |
| References | Fritz John, Partial Differential Equations. (ISBN: 978-0387906096) |
| Walter A. Strauss, Partial Differential Equations: An Introduction. (ISBN: 978-0470054567) |
Course Description
- The official course description on MATH 423 / CAAM 423 / MATH 513 / CAAM 523.
- List of Topics:
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- An introduction to PDEs and associated applications.
- First order linear and nonlinear PDE:
- Transport equation, the method of characteristics, local existence theory.
- Burgers equation, weak solution, distribution theory.
- Hyperbolic conservation laws, Riemann problem, entropy solution. - Second order linear PDE, 3 basic equations:
- Wave equation: plane wave, traveling wave and solitons, Fourier analysis.
- Laplace equation: fundamental solution, Green's function, potential theory.
- Heat equation: maximum principle, regularity. - Second order elliptic equations (if time permits):
- Sobolev spaces, weak solution, and regularity.
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: 11/18, Homework 9 is available. It is due on Tuesday 11/28 in class.
Download Homework Assignments.
Exams
- A final take-home exam will be given at the end of the semester. For MATH423/CAAM423 student, the exam will take 200 minutes. For MATH513/CAAM523 students, the exam will take 4 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 200 consecutive minutes (or 4 consecutive hours) on the exam. Please submit your exam to my office on Wednesday December 13th, between 10am-12pm, 2pm-4pm.
- Exams are under the honor code. Be sure and hand in all the work you do on each problem. Good luck!
- Last update: 12/14, the solution of the final exam is available.
- Download Exams and Solutions.
Grades
- Your grade are distributed as below:
-
Homeworks » 60% 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.