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MA371 Qualitative Theory of ODEs

In 2011-12 this module will be taught by Dr Claude Baesens - information below is from previous years...

Link UG handbook entry

Link to main Mathstuff entry. This has links to exam solutions from previous years. It also has solutions for questions on the example sheets from this year (these are in the archive section of the Mathstuff page, under last year 2009-10; in a few cases the numbers of the questions and of the solutions are slightly different, but each question has a solution).

Link to library (for past exam papers summer 2006 - summer 2010)

2010-11

The last lecture of the course was interrupted by a fire alarm. None of the material in that lecture (either the bit I did deliver, or the bit that I didn't) will come up on the exam. At the time I said I would post the notes for that lecture on this page. I am afraid that I have not done this for three reasons: (i) in the excitement I lost the notes I made for that lecture; (ii) I was afraid that if I posted the notes here it would lead some students to worry that they ought to learn the material for the exam; (iii) I got distracted by other things.

Each year I lecture slightly differently. Feel free to look at the notes produced by David Kitson in 2009-10 (link below). There were a few minor changes in detail and in content this year.

Revision (for summer 2011 exams - most recently updated March 2011)

Student Notes: David Kitson kindly texed notes from the 2009-10 lectures and allowed me to post them here (46 pages, pdf). I have spotted a few errors but mostly these will be obvious, and you will of course have your own notes in case of confusion.

The best guide to the style and content of this year's exam questions is the exam questions from recent years. (There are links to questions and to solutions at the top of this page, and there are comments on the questions further down this page). As in the past, questions will largely consist of bookwork, simple applications of bookwork, and exercises in a familiar style. I consider it is fair to ask you to do exercises that are (a) like those covered explicitly in the lectures; (b) like those on past exam papers unless the notes below say otherwise; (c) similar to those example sheet questions listed below; (d) modest variations on all of these.

The following questions from the example sheets are recommended (for education, to test your understanding, and - in some cases - as examples of the type of exercise that might occur in an exam). Copies of solutions for the example sheets are available on Mathstuff. (Question numbers in the lists below refer to this year's example sheets; in some cases the solutions are numbered slightly differently.)

Example sheet 1: 1, 2, 3, 4, 5, 6, 9, 10, 11

Example sheet 2: 1, 2, 4, 6, 8, 10, 12

Example sheet 3: 1, 2, 4, 6, 9, 10, 11, 12, 13

Example sheet 4: 1, 2, 3, 4, 5, 6, 7, 8, 9, 15

Comments on past exam questions - past questions (summers 2006-2010) are mostly a reasonable model for possible questions this year:

General: Pre-2008 questions sometimes refer to a "semi-flow". I usually referred only to "flows" and for almost all purposes forward-thinking persons can just ignore the difference.

Summer 2008, 2009, 2010: I set these papers, so they are similar in style to the paper that will be set this year. People scored well in 2008 (a little too well). 2009 seemed to be a little too hard and scores were lower. 2010 was somewhere in between, and was probably about right.

Summer 2007: I will not set a question like 4(ii), but you should be familiar with the energy balance method (computing Delta H) for showing the existence of a periodic orbit for small beta in the van der Pol equation.

Summer 2006: I will not set questions like 1(c) or 2 (we did not really cover this material in any detail in lectures).

Good luck, Colin