Course Content
The course covers introductory material from the theory of ordinary differential equations. There are three main parts of the theory of ODE's:
- finding exact solutions,
- qualitative description of solutions, and
- finding (approximate) numerical solutions.
The course concentrates on the first two.
A much more detailed outline follows. This is subject to change, depending on how the course is going.
- Introduction
- Terminology
- Order of an Equation
- Scalar Equations vs. Systems
- Linear vs Nonlinear
- Invariants
- Symmetry
- Terminology
- Examples
- Trigonometric Functions
- Elliptic Functions
- Van der Pol's Equation
- Legendre Equation
- Bessel's Equation
- Celestial Mechanics
- First Order Linear Systems
- Homogeneous Equations
- Inhomogenous Equations
- Reduction of Order
- Matrix Viewpoint
- Linear Constant Coefficient
- Matrix Exponential
- Definition
- Properties
- Computation
- Method of Undetermined Coefficients
- Inhomogeneous Equations
- Matrix Exponential
- Nonconstant Coefficients
- Examples
- Existence
- Uniqueness
- Stability
- Definitions
- Examples
- Stability Criterion for Linear Constant Coefficient Systems
- Autonomous Systems
- Linearisation
- Invariants
- Lyapunov's Method
Text
The course will roughly follow the book The Qualitative Theory of Ordinary Differential Equations, an Introduction by Fred Brauer and John A. Nohel. Buying the book is not strictly required, but it would be a good idea. It's relatively cheap at about 12 euro.
Tutorials
There are no tutorials in the usual sense.
Exams
There will be a two hour annual exam during the usual period for annual exams. This will count for 80% of your final mark for the course. More information on the date, time and location will be posted once it is available. In revising, you may find last year's annual exam, scholarship exam and supplemental exam helpful.
Assignments
There will be assignments at intervals of about two weeks. These will contribute 20% to your final mark for the course. Assignments and solutions will be posted on the course web page. The first assignment, due 23 October, is available in either PostScript or PDF formats. The solutions are also available in either PostScript or PDF formats. The second assignment, due 7 November, is available in either PostScript or PDF formats. The solutions are also available in either PostScript or PDF formats. The third assignment, due 21 November, is available in either PostScript or PDF formats. The solutions are also available in either PostScript or PDF formats. The fourth assignment, due 5 December, is available in either PostScript or PDF formats. The solutions are also available in either PostScript or PDF formats. The final assignment, due 6 February, is available in either PostScript or PDF formats. The solutions are also available in either PostScript or PDF formats.