Math 6160
Partial Differential Equations
Winter, 2019
| Instructor: |
Dr. Xiaoqiang Zhao, HH-2009, zhao@mun.ca |
| Time: |
Monday and Wednesday, 10:30-11:45am |
| Classroom: |
HH-3013 |
| Office Hours: |
Monday 13:00-14:30, Friday 10:30-12:00 |
| Course Website: |
http://www.math.mun.ca/~xzhao |
Text:
L. C. Evans, "Partial Differential Equations", second edition, American Mathematical Society,
2010.
Evaluation:
| Assignments |
40% |
| Midterm Test |
20% |
| Final Exam |
40% |
Course Contents:
- Linear Equations (Chapter 2)
- Laplace's equation
- Heat equation
- Wave equation
- Sobolev Spaces (Chapter 5)
- Sobolev spaces
- Approximations, extensions, traces
- Sobolev inequalities
- Compactness
- Second Order Elliptic Equations (Chapter 6)
- Definitions
- Existence of weak solutions
- Regularity
- Maximum principles
- Eigenvalues and eigenfunctions
Assignments:
You should do your assignments independently. The assignments
will be collected before the class starts on the due date.
No late assignments are acceptable.
Assignment 1, Due date: Wednesday, January 30
Section 2.5 (Problems): 2, 5, 6
Total points 100= 16 (P2)+ 18 (P5a) + 16*3 (P5bcd) +18 (P6)
Assignment 2, Due date: Wednesday, February 13
Section 2.5 (Problems): 13, 14, 19, 24
Total points 100= 10*2 (P13ab)+ 16 (P14) + 10*4 (P19abcd) +12*2 (P24ab)
Assignment 3, Due date: Wednesday, March 13
Section 5.10 (Problems): 11, 15
Assignment 4, Due date: Wednesday, March 27
Section 5.10 (Problems): 18; Section 6.6 (Problems): 2, 4.
Midterm Test (in class): Monday, February 25
The midterm test covers all contents we finished before the winter
semester break.
Final Exam (two hours): 10:00am-12:00, Tuesday, April 16, HH-3013