2017 Spring: Differential Equations II
English Version|中文版
Basic InformationInstructor: Professor Xing Liang, xliang@ustc.edu.cn
TA: Junyan Zhang, zhangjy9610@gmail.com
TA: Xiyu Hu, hxypqr@mail.ustc.edu.cn
Time & Location: Tue(3,4,5), Fri(1,2), @3C104 on West Campus.
PrerequisitesLebesgue Integral and Convergence Theorems, L^p spaces, Hilbert Spaces,
Weak/Weak-* Convergence, Compact Operator and its spectrum.
Textbook: Lawrence C. Evans: Partial Differential Equations, 2nd edition, AMS. Chapter 5, 6, 7. (2nd edition only!)
Download the pdf of Evans' book: Link 1. (Password: earz)
Download Ch5~7+Appendix: Link 2. (Passworf: 58dp)
Contexts:
Review of Prerequisites, Sobolev Spaces, Weak Solution Theory of Elliptic/Parabolic/Hyperbolic PDE,
Maximum Principles, Finite Propagation Speed.
Click here to download.
If there is any mistake, please feel free to let me know.
ExamsMidterm: April 21, 2017, 7:50-9:20AM.
Classroom: 3C103(JL+PB12011065-PB14000735), 3C104(PB14001007-PB14210110).
Rubric of Midterm Exam: Link.
Participants: 92, Highest Score: 109/110, Average: 66.94. 55 students got ≥66.
Average Score of each problem: 14.94/20，32.09/45，9.53/25，10.38/20.
Final: June 7th, 2017. 2:30-5:00 PM.
Classroom: 3C103(Students in SCGY), 3C104(Class 14001).
Rubric of Final: Link.
Participants: 82, Highest Score: 115/120, Average: 82.55. 60 students got ≥72.
Average Score of each problem: 19.79/20, 13.93/20, 13.91/20, 13.34/20, 8.60/15, 13.00/25.
HW
Errata of HW 2 is here.
The hint was invalid because this conclusion is needed to prove the equivalence of W^{1,∞} and being Lipschitzian.
| No. | Contexts | Due |
| Week 1-2 | Week 1-2 Complement+Ch5: 1~6 | 2.28 |
| Week 3-4 | Week 3-4 Ch5: 7, 8, 9, 18+Complement | 3.14 |
| Week 5-6 | Week 5-6 Ch5: 10, 17, 12, 19+Complement | 3.28 |
| Week 7-8 | Week 7-8 Ch6: 1-5+Complement | 4.11 |
| Week 9-11 | Week 9-11 Ch6: 6, 7, 9-13+Complement | 5.2 |
| Week 12-14 | Week 12-14Ch6: 14, 15, Ch7: 1, 2, 5-8, 9+Complement. | 5.23 |
Recitation Classes
Errata of Recitation Class 7.
I've correct the decription of Fredholm Alternative.
Also please omit the contexts about Strichartz Estimates of Parabolic Equations.
Errata of Recitation Class 1, 2.
| No. | Date | Classroom | Contexts | Download |
| 1 | 3.4 19:00-21:00 | 3C104 | Ch5, POU in R^d | Notes 1 |
| 2 | 3.18 19:00-21:00 | 3C104 | Ch5+Weak/Weak* Convergence, Compact Operators. | Notes 2 |
| 3 | 4.8 19:00-21:00 | 3C104 | Ch5, 6 | |
| 4 | 4.15 19:00-21:15 | 3C104 | Ch6+Midterm Review | Notes 4-5 |
| 5 | 5.5 07:50-09:20 | 3C104 | Ch6, Maximum Principle, Variational Method. | |
| 6 | 5.13 19:00-21:15 | 3C104 | Ch6: 13-15, Ch7: 5, 6, 9, 11 | Notes 6 |
| 7 | 6.2 07:50-09:20 | 3C104 | Ch7: 1, 2, 4, 7, 8, Review of Final. | Notes 7 |