Math 6160
Partial Differential Equations

Winter, 2024

Text:

L. C. Evans, "Partial Differential Equations", second edition, American Mathematical Society, 2010.

Evaluation:

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. No late assignments are acceptable.

  Assignment 1, Due date: Thursday, Jan. 25

  Section 2.5 (Problems): 2, 5, 6

  Total points 100= 16 (P2)+ 18 (P5a) + 16*3 (P5bcd) +18 (P6)

  Assignment 2, Due date: Thursday, Feb. 8

  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: Thursday, March 14

  Section 5.10 (Problems): 14, 16, 17, 18

  Note that in Problem 16, change $H^1(R^n)$ into $H^1_0(R^n)$; and in Problem 17, change $1\leq p\leq \infty$ into $1\leq p< \infty$ (i.e., $p$ is not infinity).

  Assignment 4, Due date: Thursday, March 28

  Section 5.10 (Problems): 11; and Section 6.6 (Problems): 1, 4, 11

  Midterm Test (in the classroom): 10:30-11:45, Tuesday, Feb. 27

  The midterm test covers the contents discussed in ALL classes before and on Feb. 13.

  Final Exam: 12:00-2:00pm, Wed., April 17, HH-3017

  The final exam covers the contents discussed in the WHOLE semester.