This page contains material for the course: MATH 971 Applied Non-Linear Differential Equations.
The lecture notes are those of the 2009 version of the course and should not be downloaded by students taking the course in 2010.
This course provides an introduction to applied non-linear ordinary differential equations. This course is applied mathematics. There will be no technical lemmas or abstract definitions!
The course typically consists of twelve two-hour lectures. Participants will spend most of their time working on example problems and tutorial sheets, often using computer packages such as maple and matlab. In some years, towards the end of the session, students are given a project to apply the ideas that they have learnt.
A set of AMSI guidelines for this course are available here.
Topics to be covered include (but are not limited to):
No knowledge of applied mathematics is assumed. Little knowledge above second year calculus is required. It will be assumed that you have used Maple previously. If you don't like Maple you are free to use an equivalent package. The main skill that is required is mathematical maturity in knowing how to approach problems.
Your final mark in MATH971 will be determined as follows. Two marks will be calculated using scheme one (S1) and scheme two (S2).
| Scheme | S1 | S2 |
| Final Exam | 60 | 50 |
| Assignments | 40 | 50 |
Your final mark will be the higher of the marks calculated using schemes one and two. Scaling of marks is not a standard procedure in this subject.
Note that you are not required to `pass' each individual component to receive a pass grade in MATH971. However, you would seriously jeopardise your chances of passing this subject if you do not aim to be successful in every component of the assessment.
Where appropriate I've listed some alternative reading that reinforces the material in each chapter.
Most of this chapter (1.1-1.5) is based upon notes from a first-year mathematical modelling course.
| B.1 | Introduction |
| B.2 | Taylor series expansion of a function of one variable |
| B.3 | Taylor series expansion of a function of two variables |
| D.1 | Transforming a planar system of differential equations from Cartesian co-ordinates to polar co-ordinates |
| D.2 | Things to do. |
| E.1 | Stationary points and the test for stationary points |
| E.2 | Questions. |
| E.3 | Things to do. |
Note that the chapter numbers have not been the same from year-to-year.
| 2008 | 2009 | |
| Week 2 | Chapter 1 | |
| Week 3 | Chapter 1 | |
| Week 4 | Chapter 2 | |
| (sections 2.1-2.3) | ||
| Week 5 | Chapter 2 | Chapter 2 |
| (section 2.4 & 2.5 | ||
| Week 7 | Chapter 3 | |
| Week 8 | Chapter 3 | |
| Week 9 | Chapter 5 | Chapter 5 |
| Week 10 | Chapter 6 | |
| Week 11 | Chapter 6 | |
| Week 12 | Chapter 7 | |
| Week 13 | Chapter 8 |
| 2008 |