PARTIAL DIFFERENTIAL EQUATIONS I: Introduction to Elliptic and Parabolic PDE

UBC Math 516, Fall 2017



Instructor: Stephen Gustafson, Math 115, phone 604-822-3138, gustaf@math.ubc.ca

Office Hours: by appointment

Course outline

Lectures:   Mon/Wed/Fri   1:00 - 1:50 in MATX 1118

  • Lecture 1 (Sep. 8): the classical linear PDE
  • Lecture 2 (Sep. 11): solution of Poisson's equation in R^n
  • Lecture 3 (Sep. 13): solution of the heat equation in R^n
  • Lecture 4 (Sep. 15): solution of the wave equation in R^n
  • Lecture 5 (Sep. 18): properties of harmonic functions: mean value; maximum principle
  • Lecture 6 (Sep. 20): properties of harmonic functions: uniqueness; regularity
  • Lecture 7 (Sep. 25): properties of the heat equation
  • Lecture 8 (Sep. 27): second-order elliptic: weak solutions
  • Lecture 9 (Sep. 29): second-order elliptic: Fredholm alternative
  • Lecture 10 (Oct. 2): second-order elliptic: interior regularity
  • Lecture 11 (Oct. 4): second-order elliptic: boundary regularity
  • Lecture 12 (Oct. 6): second-order elliptic: maximum principles
  • Lecture 13 (Oct. 13): second-order elliptic: method of sub/super-solutions
  • Lecture 14 (Oct. 18): second-order parabolic: weak solutions and energy estimate
  • Lecture 15 (Oct. 20): second-order parabolic: existence of weak solutions
  • Lecture 16 (Oct. 23): second-order parabolic: regularity of weak solutions

Homework Assignments:

Reference list


Back to S. Gustafson's homepage or UBC Math.

Last modified: Aug. 9, 2017.