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MAT 1060H:
Introduction to Partial Differential Equations

__ Professor__: Mary Pugh

__ Contact information__: mpugh@math. utoronto.ca

__ 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'.

**
Syllabus: **

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.