Course Information
| Instructor | Dr. Changhui Tan |
| Lectures | Tu Th 9:25am - 10:40am, at HBH 227 |
| Office | HBH 328 |
| Office Hours | Tu Th 10:40am - 11:40pm, or by appointment |
| Teaching Assistants | Andy Huang, at HBH 45. This email address is being protected from spambots. You need JavaScript enabled to view it., at HBH 14. |
| TA Office Hours | M W 3pm - 4pm, at either HBH 45 or HBH 14. |
| Textbooks (Required) | 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/CAAM 423.
- List of Topics:
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- First order linear and nonlinear PDE:
- Transport equation, method of characteristics, local existence theory. - Second order linear PDE, 3 basis equations:
- Wave equation: causality and energy, plane wave, traveling wave and solitons.
- Laplace equation: fundamental solution, Green's function, potential theory.
- Heat equation: maximum principle, regularity. - Second order elliptic equations:
- Sobolev spaces, weak solution and regularity. - Asymptotic methods:
- the method of stationary phase, geometrical optics, singular perturbation methods. - Selected topics (if time permits):
- Hamilton-Jacobi equations and calculus of variations
- Hyperbolic conservation laws
- First order linear and nonlinear PDE:
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: 11/24, Homework 13 is available, due on Thursday 12/3 in class.
Download Homework Assignments.
Exams
- There will be one midterm exam and one final exam (at the end of semester).
- The midterm exam is a 2-hour exam with a total of 110 points. You can also choose to finish it in 3 hours. If so, 10 Points will be deducted, and the total will be 100 points. 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 2 consecutive hours on the exam.
- The final exam is a 3-hour exam with a total of 110 points. You can also choose to finish it in 4 hours. If so, 10 Points will be deducted, and the total will be 100 points. 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 (or 4) consecutive hours on the exam. Please submit your exam to my office on Monday December 7th, between 10am-12pm, 2pm-4pm.
- Exams are under honor code. Be sure and hand in all the work you do on each problem. Good luck!
- Last update: 12/14, the solution for final exam is available.
- Download Exams and Solutions.
Grades
- Your grade are distributed as below:
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Homeworks » 40% Midterm exam » 25% Final exam » 35%
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. Or you can leave a comment below.