Math 517 -- Partial Differential Equations -- Fall 2024

The instructor is Professor Yanyan Li.

Office Hour: Monday 3:50-5:10pm

Final Exam will be a take home exam. Final exams problems will be given by Nov. 20. The final exam will be due on Dec. 2, and handed in paper form.


Textbook

Evans' book "Partial Differential Equations" (second edition);


Policy

Homework (50%); Final Exam (50%).

Hand in homework every Monday for homework assignment of previous week.


Tentative Syllabus and homework

Date Section Homework
Sept. 4 2.1, Transport equations Graded homework: Page 85, #1. Not graded homework: Assigned in class.
Sept. 9 2.2, Laplace's equation Graded homework: Page 85, #2.
Sept. 11 2.2, Laplace's equation Graded homework: Page 85, #3, 4, 5. Not graded homework: Page 85, #6.
Sept. 16 2.2, Laplace's equation Graded homework: P87, #11. Not graded homework: #2.8 of [Gilbarg-Trudinger book].
Sept.18 2.2, Laplace's equation
Sept. 23 2.2, Laplace's equation
Sept. 25 2.2, Laplace's equation Graded homework: Page 86, #7, 8. Not graded homework: Page 86, #9, 10.
Sept. 30 2.2, Laplace's equation; 2.3, Heat equation Graded homework: Page 87, #12, 13.
Oct. 2 2.3, Heat equation Graded homework: Page 87, #14, 15.
Oct. 7 2.3, Heat equation Graded homework: Page 88, #16, 17.
Oct.9 2.3, Heat equation
Oct. 14 2.3, Heat equation Not Graded homework on isolated singularity of harmonic functions.
Oct. 16 2.4, Wave equation Graded homework: Page 88, #18, 19. Not graded homework: Page 87, #15.
Oct. 21 2.4, Wave equation Not Graded homework: Page 89, #20, 21, 22.
Oct. 23 2.4, Wave equation Gave a final exam problem.
Oct. 28 Chapter 5: Sobolev spaces. 5.1, Holder spaces. Graded homework: Page 305, #1,2,3. Not graded homework, P 305, #4.
Nov. 4 5.2, Sobolev spaces Graded homework: Page 307, #11, 12, 13, 14. Gave a final exam problem.
Nov. 6 5.2, Sobolev spaces Graded homework: Page 305-306, #5, 6, 9, 10.
Nov. 11 5.2, Sobolev spaces Graded homework: Page 307, #11, 12, 13, 14; Not Graded homework: Page 307, #15, 17, 18.