MA303-6-AU: ORDINARY DIFFERENTIAL EQUATIONS
Department: Mathematical Sciences
Essex credit: 15
ECTS credit: 7.5
Available to Study Abroad / Exchange Students: Yes Full Year Module Available to Study Abroad / Exchange Students for a Single Term: No Pre-requisites: MA104 AND MA118 AND MA206
|Module is taught during the following terms
The course provides an overview of standard methods for the solution of single ordinary differential equations and systems of equations, with an introduction to some of the underlying theory.
Definitions. First-order differential equations:
Second-order differential equations.
reduction of order, constant coefficients;
second-order linear equations: ordinary points and regular singular points.
Series solutions of second-order linear differential equations.
Power series, solutions about an ordinary point.
Solutions about a regular singular point.
Equal roots of indicial equation and roots differing by an integer.
Introduction to systems of first-order equations.
Two linear first-order equations.
Non-linear differential equations and stability.
Autonomous systems: trajectories in the phase plane, critical points.
Stability and asymptotic stability.
Linear and almost linear systems; classification of critical points.
Competing species and predator-prey problems.
On completion of the course students should be able to:
- use some of the standard methods for solution of first- and second-order ordinary differential equations;
- be aware of the implications of existence and uniqueness theorems;
- solve systems of linear first-order equations in two unknowns with constant coefficients;
- analyse the stability characteristics of non-linear systems in two unknowns.
Learning and Teaching Methods
This course runs at 3 hours per week. There are 5 lectures and one class in every fortnight.
In the Summer term 3 revision lectures are given.
20 per cent Coursework Mark, 80 per cent Exam Mark
There are 2 coursework tests worth 10% each.
Information about coursework deadlines can be found in the "Coursework Information" section of the Current Students, Useful Information Maths web pages: Coursework and Test Information
Exam Duration and Period
2:00 hour exam during Summer Examination period.
Available to Socrates /IP students spending all relevant terms at Essex.
- Essential Reading:
J. R. Brannan and W. e. Boyce, Differential Equations with Boundary Value Problems: Modern Methods and Applications (2nd edition), Wiley Interscience (2011)
W.E. Boyce and R.C. Di Prima, Elementary Differential Equations and Boundary Value Problems, Wiley
E. A. Coddington, An Introduction to Ordinary Differential Equations, Dover Publications (1989)
D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations. An Introduction for Sceintists and Engineers, Oxford University Press (2007)
D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: Problems and Solutions - A Sourcebook for Scientists and Engineers, Oxford University Press (2007)