# Math 319

**Announcement**:

If you want to have a look at your exam paper before the grades become official please come by my office on **Monday** between **10:30-13:00**. The grades will be submitted to administration Monday afternoon.

**Lectures**

**MTR 11:35–12:25**,
Burnside Hall 1B39

**Instructor**

Dr. Gantumur Tsogtgerel

Office: Burnside Hall 1123. Phone: (514) 398-2510. Email: gantumur -at- math.mcgill.ca.

Office hours: **Thursdays 14:00–16:00**

**Catalog description**

First order equations, geometric theory;
second order equations, classification;
Laplace, wave and heat equations,
Sturm-Liouville theory, Fourier series,
boundary and initial value problems.

**Topics to be covered**

Brief review of some relevant topics from linear algebra, calculus and ordinary differential equations.
Introduction to (partial) difference equations
Derivations of some important equations of mathematical physics.
Fourier series. Orthonormal bases for function spaces. Integral transforms.
Cauchy problems for the heat and wave equations.
Fundamental solutions.
Separation of variable method for solving various (initial-) boundary value problems.
Introduction to numerical methods for solving partial differential equations.
Conservation laws (as time permits).
Green's functions (as time permits).

**Prerequisites**

MATH 223 (Linear algebra) or MATH 236 (Algebra 2),

MATH 314 (Advanced calculus),

MATH 315 (ODE).

**Recommended books**

I suggest you to pick 1 or 2 books from the following list and work your way through them.

Charles R. MacCluer. Boundary value problems and Fourier expansions. Dover 2004
Stanley J. Farlow. Partial differential equations for scientists and engineers. Dover 1993
David Colton. Partial differential equations: An introduction. Dover 2004
J. David Logan. Applied partial differential equations. Springer 2004
Paul DuChateau and David Zachmann. Applied partial differential equations. Dover 2002
E. C. Zachmanoglou and Dale. W. Thoe. Introduction to partial differential equations with applications. Dover 1986
Donald Greenspan. Introduction to partial differential equations. Dover 2000

**Homework Assignments**

Assigned and graded roughly every two weeks.
All homework assignments will count towards the final grade. Late homeworks will not be accepted.

**Exams**

There will be a take-home midterm exam and a centrally scheduled final exam.
The final exam is tentatively scheduled on Monday **April 11, at 6pm**.
You are allowed to bring one (double-sided) sheet of hand-written notes to the final exam.

**Grading**

Homeworks 20%, the take-home midterm 30%, and the final exam 50%.