Content
After a quick introduction the topics considered will be
introduction,
definitions, terminology and notation,
quick review of multivariable calculus, linear algebra,
numerical solution methods,
general existence and uniqueness theorems,
linear equations,
separable and integrable equations,
stability for autonomous systems,
not necessarily in that order.
Text
There is no textbook for the course. Slides from the lectures are available below.
Online Lectures
Due to the Covid-19 outbreak all lectures this semester will be online. I plan to post them here and on Blackboard. The Blackboard versions are closed captioned for the hearing impaired, anyone listening in a noisy environment, or anyone who prefers not to listen to the sound of my voice. Blackboard's automatic captioning is terrible though.
| Lecture | Date | Topic(s) | Video | Slides |
|---|---|---|---|---|
| 1 | 15 September 2021 | Introduction and Examples | Video | Slides |
| 2 | 16 September 2021 | Terminology | Video | Slides |
| 3 | 17 September 2021 | Reduction of order, invariants | Video | Slides |
| 4 | 22 September 2021 | Existence and uniqueness | Video | Slides |
| 5 | 23 September 2021 | Numerical solution | Video | Slides |
| 6 | 24 September 2021 | Review of linear algebra | Video | Slides |
| 7 | 29 September 2021 | Calculus of vector and matrix valued functions I | Video | Slides |
| 8 | 30 September 2021 | Calculus of vector and matrix valued functions II | Video | Slides |
| 9 | 1 October 2021 | Introduction to linear differential equations | Video | Slides |
| 10 | 6 October 2021 | Fundamental solutions | Video | Slides |
| 11 | 7 October 2021 | Basic solutions | Video | Slides |
| 12 | 8 October 2021 | Undetermined coefficients | Video | Slides |
| 13 | 13 October 2021 | Matrix exponentials I | Video | Slides |
| 14 | 14 October 2021 | Matrix exponentials II | Video | Slides |
| 15 | 15 October 2021 | Proofs, a 4x4 example, and an alternate method | Video | Slides |
| 16 | 20 October 2021 | Behaviour as t tends to infinity | Video | Slides |
| 17 | 21 October 2021 | Examples | Video | Slides |
| 18 | 22 October 2021 | First order scalar equations, Green's functions | Video | Slides |
| 19 | 3 November 2021 | Change of variable for linear equations, partially decoupled equations | Video | Slides |
| 20 | 4 November 2021 | Wronskian reduction of order, power series solutions | Video | Slides |
| 21 | 5 November 2021 | Separable equations | Video | Slides |
| 22 | 10 November 2021 | Introduction to stability | Video | Slides |
| 23 | 11 November 2021 | Examples | Video | Slides |
| 24 | 12 November 2021 | Stability of linear autonomous systems | Video | Slides |
| 25 | 17 November 2021 | Lyapunov theory | Video | Slides |
| 26 | 18 November 2021 | Examples | Video | Slides |
| 27 | 19 November 2021 | Determining stability from the linearisation | Video | Slides |
| 28 | 24 November 2021 | Existence and uniqueness I | Video | Slides |
| 29 | 25 November 2021 | Existence and uniqueness II | Video | Slides |
| 30 | 26 November 2021 | Existence and uniqueness III | Video | Slides |
| 31 | 1 December 2021 | Module overview, exam information | Video | Slides |
Exams
There was an exam in December. Information on the date, time and venue of it and of any supplemental exams is available from the Exams Office.
Assignments
There will be a small number of marked assignments, worth 20% of your module mark.
| Assignment | Date Posted | Date Due | Questions | Answers |
|---|---|---|---|---|
| 1 | 4 October 2021 | 11 October 2021 | Problems | Solutions |
| 2 | 3 November 2021 | 12 November 2021 | Problems | Solutions |
There will also be practice problems, roughly weekly, which will not be marked but solutions will be posted so that you can check your answers.
Tutorials
There are no tutorials scheduled for this module. I may occasionally use one of the scheduled lecture slots as a pseudotutorial as needed.
Practice Problems
I will post practice problems approximately weekly. This will not be marked, but I will posted solutions so you can check your work.
| Problem Set | Date Posted | Lectures Covered | Problems | Solutions |
|---|---|---|---|---|
| 1 | 20 September 2021 | 1-3 | Problems | Solutions |
| 2 | 27 September 2021 | 4-6 | Problems | Solutions |
| 3 | 12 October 2021 | 7-11 | Problems | Solutions |
| 4 | 20 October 2021 | 12-15 | Problems | Solutions |
| 5 | 17 November 2021 | 16-20 | Problems | Solutions |
| 6 | 24 November 2021 | 21-25 | Problems | Solutions |
Discussion board
There is a discussion board available in Blackboard, which you can use to ask any questions you have.
Links to past exam papers
Various past TCD exam papers for Ordinary Differential Equations, under a variety of different module codes, are available online. Due to changes in content, terminology, notation, etc. some past questions, or parts of questions, would not be appropriate for the current version of the module.
| Academic year | Module Code | Instructor | Questions to ignore |
|---|---|---|---|
| 2020-2021 | MAU23205 | John Stalker | |
| 2019-2020 | MAU23205 | Gurpreet Singh | 1c,2a,2b,4a |
| 2018-2019 | MA2327 | Miriam Logan | 1a |
| 2017-2018 | MA2327 | John Stalker | |
| 2016-2017 | MA2327 | Paschalis Karageorgis | 2b |
| 2015-2016 | MA2327 | John Stalker | 1b |
| 2014-2015 | MA2326 | John Stalker | 3b |
| 2013-2014 | MA2326 | John Stalker | 1b |
| 2012-2013 | MA2326 | Petronela Radu | 1a,1b,1c,4a,4b,5a |
| 2011-2012 | MA2326 | Esther Vergara Diaz | 2c,3c,4b,5a |
| 2010-2011 | MA2326 | Paschalis Karageorgis | 2b, 2c |
| 2009-2010 | MA2326 | Paschalis Karageorgis | |
| 2008-2009 | 216 | Paschalis Karageorgis | 5a |
| 2007-2008 | 216 | John Stalker | |
| 2006-2007 | 216 | John Stalker | |
| 2005-2006 | 261 | Adrian Constantin | 6,7,8 |