The course will cover the following topics:
- Terminology (order, scalar vs. system, linear vs. nonlinear, invariant)
- Separable equations, exact equations, first order linear equations
- Linear constant coefficient equations, exponential of a matrix
- Undetermined coefficients, variation of parameters
- Successive approximation, existence and uniqueness of solutions
- Autonomous systems, stability, Lyapunov functions
Text
There is no official textbook for the course. Books on Ordinary Differential Equations tend to be largely interchangeable.
It is hard to find a full treatment of the existence and uniqueness theory and related topics. I've prepared some notes which cover more than I will have time to discuss in lecture. There are three, very brief, chapters: 0, 1, 2. Chapter 0 contains some logical and set theoretic material which is used in Chapter 1. I would advise skipping until after reading Chapter 1, and possibly skipping it entirely.
Exams
There will be single exam during the usual annual exam period, worth 80% of your course mark. We are not allowed to announce exam dates and locations on course web pages, but there will be a link here to the official schedule once that is available. A sample paper will be made available towards the end of the course.
Assignments
Assignments will count for 20% of your course mark. They will be posted here, roughly weekly, and will be due at the beginning of the Tuesday afternoon lecture. They will not be distributed in class. Solutions will be posted here once the assignment has been corrected.
| Assignment | Due | Version | Problems | Solutions |
|---|---|---|---|---|
| 1 | 27 January 2015 | Id: 2326-s2015-1.m4,v 1.3 2015/01/22 20:39:22 john Exp john | PS PDF | PS PDF |
| 2 | 3 February 2015 | Id: 2326-s2015-2.m4,v 1.3 2015/01/30 11:20:59 john Exp john | PS PDF | PS PDF |
| 3 | 10 February 2015 | Id: 2326-s2015-3.m4,v 1.1 2015/02/02 20:37:30 john Exp john | PS PDF | PS PDF |
| 4 | 17 February 2015 | Id: 2326-s2015-4.m4,v 1.2 2015/02/25 11:47:51 john Exp john | PS PDF | PS PDF |
| 5 | 5 March 2015 | Id: 2326-s2015-5.m4,v 1.1 2015/02/25 11:47:26 john Exp john | PS PDF | PS PDF |
| 6 | 19 March 2015 | Id: 2326-s2015-6.m4,v 1.1 2015/03/11 22:35:58 john Exp john | PS PDF | PS PDF |
| 7 | never | Id: 2326-s2015-7.m4,v 1.1 2015/04/17 21:39:06 john Exp john | PS PDF | PS PDF |
Tutorials
There are no tutorials scheduled for this course. I will sometimes take some time out from lecture to discuss a recent assignment or, less often, the current assignment, but usually I will just rely on you reading the posted solutions and paying attention to any hints given in the statement of the problems.
Past Courses
Last year's MA 2326, also taught by me, was very similar to this year's, as you can see from its course web page. The previous year's 2326 web page appears to have vanished. The previous year's course, taught by Paschalis Karageorgis, covered essentially the same material as this one. My old course web pages from 2007 and 2008 are more of a historical curiosity than a useful source of information, since the course has changed since then.