Instructor: Gordon Craig
Office: Burnside Hall 1243
Office Hours: Monday/Thursday 12:00-2:00 pm, and by
appointment. I will also be available to answer questions after
class.
I'll schedule
some special office hours before the midterm and the final.
Email:
craig@math.mcgill.ca
Web: http://www.math.mcgill.ca/~craig
Textbook: Boyce and di Prima, Elementary Differential Equations
and Boundary Value Problems. (Any Edition will do.) There are 8 copies of
the current(seventh) edition on reserve at the PSE library.
Lectures: Monday through Friday 9:00 am to 11:00 am, in
MacDonald Engineering 280
Grading. The course grade will be computed as follows:
Homework:
10%
Midterm: 30%
Final exam: 60%
The final exam will be held on Tuesday, May 28 at 2:00 pm in Burnside Hall 1B45. I'll set up some review sessions on the 24th, 27th and 28th.
I'll be writing the homework assignments myself. Their main purpose is to help you learn the material and to allow me to see how you're handling the material. One of the difficulties with the textbook problems is that you can normally figure out how to approach a question based on which section of the book it is from.
The purpose of this course is to give you a solid foundation in differential equations. I'll attempt to point out why they are so important, and to give you some insight into how to study them. I'll discuss some theoretical issues, but we'll spend most of our time learning how to solve equations. The equations that are explicitly solvable are quite limited, but they include some very important examples, and they allow us to model more complicated cases.
The lectures will follow the topics in the textbooks, although the approach and emphasis will be quite different. You'll get a lot more out of the lectures if you read the sections that we will be covering before coming to class. Try to at least skim over them. It's also important that you work through the problems in the textbook, and avoid looking at the solutions until you're either fairly confident that you have the right answer or are completely stumped. For better or worse, the only way to learn math is to take the time to think things through yourself. If you have any questions about anything, please email me or come to the office hours.
The pace of this course is extremely fast. We'll be covering the equivalent of a whole term in under a month, and it's very easy to fall behind. I know that a lot of you are working outside of school and/or exhausted from the previous term, but you can't allow yourself to fall behind, or else you'll have a very hard time catching up.
Handouts:
I'll use this page to keep students abreast of what we're doing in class. I'll write which sections I'm hoping to cover in each class, and then within 24 hours I'll make whatever changes are necessary to reflect what we actually accomplished. The chapter numbers refer to the seventh edition of Boyce and Di Prima, but you should be able to figure out what they correspond to previous editions without much effort.
Wednesday, May 1: Introduction(Chapter 1), First order linear equations
(2.1)
Thursday, May 2: Separable equations, substitution;
first-order homogeneous equations(2.2), Modeling with first
order equations(2.3)
Friday, May 3: Nonlinear vs. linear equations,
Bernoulli equations(2.4), Autonomous
equations, qualitative behaviour(2.5), Exact equations(2.6).
Monday, May 6: Qualitative behaviour of equations(2.5), Exact equations(2.6)
Tuesday, May 7: Exact equations(2.6), Introduction to
second order equations, second-order linear homogeneous
equations, special cases of second-order equations(3.1).
Wednesday, May 8: Fundamental solutions of second order linear
homogeneous equations(3.2), Linear independence and the Wronskian(3.3)
Thursday, May 9: Complex and repeated roots of the characteristic
equation, reduction of order(3.4, 3.5).
Friday, May 10: Repeated roots(3.5), Nonhomogeneous equations,
method of undetermined coefficients(3.6)
Monday, May 13: Undetermined coefficients(3.6), Variation of paramters(3.7)
Tuesday, May 14: Mechanical and electrical vibrations(3.8), Forced
vibrations(3.8)
Wednesday, May 15: Midterm on Chapters 2 & 3.
Thursday, May 16: Higher order linear equations(4.1, 4.2, 4.3).
Friday, May 17: Series solutions near an ordinary point(5.2, 5.3)
Monday, May 20: Victoria Day/Fête de Dollard: no class.
Tuesday, May 21: Euler equations, Regular singular points, Series
solutions near a regualr singular point(5.4, 5.5, 5.6).