The course will cover the following topics:
- Terminology and Notation
- Review of ODE
- First order scalar equations
- The Calculus of Variations
- Numerical Methods
- Free boundary problems for fluids
Text
There is no official textbook for the course, but there are notes for most of the material. I will largely follow Julie Levandovsky's notes on first order scalar equations. I will also partly follow her notes on the Calculus of Variations. I will treat Noether's theorem following the treatment in her paper. You might prefer to read an English translation. The source code of the example I used to illustrate numerical instability is available, but don't feel obligated to look at it. For free boundary problems I will follow the treatment in Birkhoff's Hydrodynamics. That book is nearly impossible to find, so I have scanned Chapter 1 (Hydrodynamical Paradoxes) and Chapter 2 (Free Boundary Theory). We will only cover the first third to a half of each, but the rest is interesting and worth reading if you have time. I am also posting a worked example of the complex hodograph method which was too complicated to do in lecture.
Exams
There will be single exam during the usual annual exam period, worth 90% 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 is available for revision. I'm posting this somewhat reluctantly, since the questions differ considerably, for obvious reasons, from those of the real exam. As long as you don't focus too narrowly on the specific questions asked it should be a reasonable guide the format and topics of real exam. I will not be posting solutions.
Assignments
Assignments will count for 10% of your course mark. They will be posted here, sporadically, and will be due at the beginning of the Wednesday 12:00 lecture. They will not be distributed in class. Solutions will be posted here once the assignment has been corrected. There is a final assignment, which will not be corrected or marked, covering the material from the last part of the course. This is meant for revision.
| Assignment | Due | Version | Problems | Solutions |
|---|---|---|---|---|
| 1 | 12 February 2014 | Id: 342H-s2014-1.m4,v 1.1 2014/02/05 11:14:01 john Exp john | PS PDF | PS PDF |
| 2 | 5 March 2014 | Id: 342H-s2014-2.m4,v 1.2 2014/04/01 23:12:19 john Exp john | PS PDF | PS PDF |
| 3 | 2 April 2014 | Id: 342H-s2014-3.m4,v 1.2 2014/04/24 10:40:59 john Exp john | PS PDF | PS PDF |
| 4 | never | Id: 342H-s2014-4.m4,v 1.3 2014/04/26 18:24:58 john Exp john | PS PDF | PS PDF |
Tutorials
There are no tutorials scheduled for this course.
Past Courses
Although I've taught MA3425 and MA3426 in the past, this is my first time teaching MA342H. 342H was last taught in 2012 by Paschalis Karageorgis. His module web page is fairly minimalist, but you may find it helpful. The overlap is about 50% with the current version.