MAT 1060H: Introduction to Partial Differential Equations

Professor: Mary Pugh
Contact information: mpugh@math.
Office hours: Mondays 10:10-12:00
Office location: room 3141, Earth Sciences Centre, 22 Russell Street (To find my office, enter the building on the Northwest corner of Huron and Russell. Get to the third floor. Walk as far south as you can. Now walk as far west as you can.)

Meeting time and place: The class meets in Sidney Smith 5017A for three hours a week: Wednesdays 1:10-2:00 and Fridays 1:10-3:00. The first lecture will be on Friday September 10 and the last on Wednesday December 8.

Goal: This one-semester course is a basic introduction the the theory of partial differential equations. It is intended to help students get up to speed for the topics in PDEs courses being taught in the spring: "Asymptotic Methods for PDEs", "Nonlinear Schroedinger Equations", "General Relativity".

Prerequisites: either you should have taken a course on measure and integration or you should be willing to suspend disbelief when presented with things like the Cauchy-Scwartz inequality and the Dominated Convergence Theorm.

On sending me email: If you're going to send me email, please include "mat1060" in the subject line. Otherwise, my spam filter will catch your email.

Textbook: The textbook is "Partial Differential Equations" by Lawrence C. Evans. Errata in the text: first printing (1998), second printing (1999), and third printing (2002). It's in stock at the campus bookstore. In addition, I've asked the Math library to put it on reserve along with the supplementary texts: "Partial differential equations" by Fritz John and "Partial differential equations: an introduction" by Walter Strauss. John's book is at the same level as Evans' but has a different approach. Strauss' book is at the undergraduate level and is more accessible if you're having difficulty with Evans'.

Chapter 2: Four Important Linear PDES
2.1 Transport equation
2.2 Laplace's equation
2.3 Heat equation
2.4 Wave equation

Chapter 3: Nonlinear First-Order PDE
3.2 Characteristics
3.4 Conservation Laws

Chapter 4: Other ways to represent solutions
4.1 Separation of variables
4.2 similarity solutions
4.3 Transform methods

Chapter 6: Second-order elliptic equations
6.1 definitions
6.2 existence of weak solutions
6.3.1 regularity
6.4 maximum principles
6.5.1 eigenvalues and eigenfunctions

Chapter 7: Linear evolution equations
7.1 second-order parabolic (if time remains)

  • Lecture Notes: Sept 10, 2004
  • Lecture Notes: Sept 15, 2004
  • Lecture Notes: Sept 17, 2004
    First homework assignment: problems 4, 5, and 7 from pages 86-87. Due Sept 29.
  • Lecture Notes: Sept 24, 2004
  • Lecture Notes: Oct 1, 2004
  • Lecture Notes: Oct 6, 2004
    Second homework assignment: this problem and problems 12, 13, and 14 from pages 87-88. Due at noon on Oct 18 in my math dept mailbox.
  • Lecture Notes: Oct 8, 2004
  • Lecture Notes: Oct 20, 2004
    Third homework assignment: problems 15, 17, and 18 from pages 88-89. Due at 5 pm on Monday Nov 3 in my math dept mailbox.
  • Lecture Notes: Oct 22, 2004
  • Lecture Notes: Oct 27, 2004
  • Lecture Notes: Oct 29, 2004
  • Lecture Notes: Nov 3, 2004
  • Lecture Notes: Nov 5, 2004
  • Lecture Notes: Nov 10, 2004
    Fourth homework assignment: these problems and problem 3 from page 163. Due at 5 pm on Wednesday Nov 17 in my math dept mailbox.
  • Lecture Notes: Nov 12, 2004
  • Lecture Notes: Nov 17, 2004 Updated Nov 21.
  • Lecture Notes: Nov 24, 2004
  • Learn more about solitons!!
  • Lecture Notes: Nov 26, 2004
    Fifth homework assignment: Due at 5 pm on Monday December 6.
    Here is the matlab code I used to generate the solutions I presented in class, along with the data and instructions on how to view it using matlab.
    I owe you an hour of class, to make up for the class I cancelled on Oct 27. We'll have class from 1:10 to 3:00 on Weds Dec 8.
  • Lecture Notes: Dec 3, 2004 Updated after class on Dec 3.
  • Lecture Notes: Dec 8, 2004

    Some Interesting Courses Next Semester:
    Mat 1501HS: Geometric Measure Theory and the Calculus of Variations, by R. Jerrard.
    Mat 1507HS: Asymptotic Methods for PDE, by V. Buslaev.
    Mat 1508HS: Nonlinear Schroedinger Equations, by J. Colliander.
    Mat 1700HS: General Relativity, by A. Butscher.