(Winter, 2010)

**Course Objectives:**
This is an introductory course on mathematical analysis of partial differential
equations. We will mostly concentrate on analytical solutions of first-order and
second-order linear equations, which include the wave, heat, and Laplace equations.
Whenever possible, we will develop techniques which produce explicit, closed-form solutioins of
these classical equations. Introduction to existence, uniqueness, and qualitative analysis
of solutions of these equations is also developed.
Lectures contain both the results and the derivations. Assignments include analytical
problems of different levels. Computer demonstrations of solutions of
partial differential equations are accessed via
links to web-enabled interactive software.

**Topics:**
First order equations, well-posedness, characteristics, wave equation,
heat equation, Laplace equation, boundary conditions, Fourier series, applications.

**Instructor:**

Dr. Dmitry Pelinovsky, HH-422, ext.23424,
e-mail: dmpeli@math.mcmaster.ca

*Office hours:* Wednesday, Thursday (11:30-12:30), or by appointment

**Teaching Assistant:**

Jason Haradyn, HH-303, e-mail: haradyjd@math.mcmaster.ca

*Office hours:* Tuesdays (13:30-15:00), behind the math cafe.

**Hours:**

*Lectures:* Monday, Wednesday, Thursday (10:30-11:20); BSB/136

*Tutorial:* Tuesday (12:30-13:20); JHE/A102

**Textbook:**

*"Applied Partial Differential Equations with Fourier series and Boundary Value Problems"*
by R. Haberman, Fourth edition (Prentice Hall, 2004), ISBN 0-13-065243-1.

**Lectures and Tutorials:**
There will be three lectures and one tutorial per week.
The lectures will be used to present new material. The tutorial will be devoted to
solving recommended problems and reviewing material for assignments and midterms.
Answers to recommended problems are also given in the textbook. The lecture and tutorial
times can be interchanged in exceptional cases, which will be anounced in class and on
webpage.

**Assignments:**
Six home assignments will be posted on the course webpage every second
week. The assignments are to be dropped in the course locker any time before
and on the date of the deadline. Only five best results are accounted in the final mark.
Solutions to assignments will be posted on the course webpage.
You may discuss problems of the assignments with each other, but we expect you to write up
the answers by yourself. You may not copy another student's solution.

**Class Tests:**
There will be two class tests on Thursdays: February 4 and
March 11. Only the McMaster standard calculator Casio fx-991
is allowed on the tests. You must bring your student
ID to the test room. Solutions to tests will not be posted on the course webpage.
Tests will involve both theory and examples, but will not include proofs of theorems.

**Final Exam:** The course is completed by a three-hour
final examination. The date and location of the final exam
will be announced by the registrar's office before the end of term.

**Marking scheme:**

Final exam (3 hrs) - 40%

Class tests (50 min - two) - 40%

Homework assignments (best five) - 20%

**Senate Policy Statement:** The course is regulated under
the following documents:
Statement on Academic Ethics
and Senate Resolutions on Academic Dishonesty. Any student
who infringes one of these resolutions will be treated according
to the published policy. In particular, academic dishonesty includes
(1) plagiarism, e.g. the submission of work that is not one's own,
(2) improper collaboration in group work on home assignments,
(3) copying or using unauthorized aids tests and examinations. It is
your responsibility to understand what constitutes academic dishonesty,
refering to Academic Integrity Policy.

**Additional information:**
Late assignments will not be marked. No make-up tests will be scheduled.
Exemptions from the tests and assignments for valid reasons are possible, but must
be requested through the office of the Associate Dean of the Faculty
you are registered with. In the event of an exemption, your course grade
will be re-weighted by increasing the weight of the final examination
to compensate for the missed test or assignment.