(Winter, 2002)

**Course Objectives:**
The course sets up a ground in mathematical analysis of partial differential
equations, with emphasis on analytical solutions of first-order and
second-order linear equations. Lectures contain both the results and the
derivations, while assignments are based on a mixture of standard
and non-trivial analytical problems. The fun part includes short in-class
quizzes and optional (bonus) web-browsing work on visualization of partial
differential equations. The course serves as an excellent bridge to any of
the three next-level courses: advanced mathematical analysis of PDEs (Math4GG3),
numerical methods for PDEs (Math4Q03) and applied nonlinear PDEs in physics
and engineering (Math742).

**Topics:**
first-order equations, second-order equations (waves, diffusions and potentials),
fundamental solutions in infinite space, Fourier methods for finite intervals,
Green's functions for non-homogeneous boundary-value problems,
and general Fourier solutions in two dimensions.

**Instructor:**
Dr. Dmitry Pelinovsky, BSB-204, ext.23424

e-mail: dmpeli@math.mcmaster.ca; http://dmpeli.math.mcmaster.ca

**Teaching Assistant:**
Somasundaram Silogini, GS-221, ext. 23627

e-mail: silogini@math.mcmaster.ca

**Hours:**

*Lectures:* Monday, Thursday (9:30-10:20); JHE/A102

*Lectures:* Tuesday (10:30-11:20); JHE/A102

*Office hours:* Tuesdays (11:30-12:30),
Thursdays (15:30-16:30), or by appointment

**Main textbook:**

*"Partial Differential Equations: an introduction"*
by W.A. Strauss, (John Wiley, 1992)

**Optional textbooks:**

*"Elementary Applied Partial Differential Equations"*
by R. Haberman (Prentice Hall, 1998)

*"Partial Differential Equations and Boundary-Value Problems"*
by N. Asmar (Prentice Hall, 2000).

**Assignments:**
Five home assignments will be handed out in class on Mondays every second
week, starting the week of January 14. The assignments are due
at 11:20 on Tuesdays in the following week. The texts for assignments
and solutions will be posted on the course webpage.

**Class quizzes:**
Five class quizzes will be held in the last 15 minutes of classes
on Thursdays every second week, starting the week of January 14.
Solutions to the quizzes will be posted on the course webpage.

**Class Test:**
There will be one class test during the regular lecture hour
on Tuesday: February 12.

**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 in mid-term.

**Marking scheme:**

Final exam (3 hrs) - 30% Class test (50 min) - 20% 5 class quizzes (15 min) - 10% 5 homework assignments - 40% |