Methods of Applied Mathematics

(Winter, 2004)

**Course Objectives:**
The course covers mathematical analysis of applied nonlinear
partial differential equations. The material focuses on
well-posedness of hyperbolic, elliptic, and parabolic equations,
which includes existence, uniqueness and stability of solutions.
Lectures contain both results and derivations.
All assignments are home-taken and based on a number of
analytical problems.

**Topics:**
quasi-linear first-order systems of equations;
elliptic, parabolic, and hyperbolic second-order equations;
applied nonlinear equations in one, two and three space dimensions,
methods of analysis: characteristics, Riemann invariants,
spectral transforms, variational and maximum principle,
Green's functions, Riemann-Hilbert problems, inverse scattering
transform.

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

**Hours:**

*Lectures:* Monday (10:30-12:00), Thursday (9:30-11:00); HH/207

*Office hours:* Tuesday, Thursday (9:30-11:30), or by appointment

**Textbooks:**

*"Applied Partial Differential Equations"*
by J. Ockendon, S. Howison, A. Lacey, and A. Movchan (Oxford University Press, 1999)

*"Partial Differential Equations"*
by F. John (Springer-Verlag, 1998)

**Assignments:**
Four home assignments will be handed out in class on Mondays every third
week, starting the week of January 12. The assignments are due
on Thursdays in the following week. The texts for assignments
and solutions will be posted on the course webpage.

**Project:** The course is completed by a take-home project.
Details of the project will be announced in mid-term.

**Marking scheme:**

Project - 40% Assignments - 60% |