Module Details

MA303-6-AU-CO: Ordinary Differential Equations

Year: 2017/18
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
Outside Option: Yes
Pre-requisites: MA104 and MA118 and MA206

Supervisor: Dr Georgi Grahovski
Teaching Staff: Dr Georgi Grahovski, email; Prof Edd Codling, email
Contact details: Miss Claire Watts, Department Manager. email:, tel 01206 873040

Module is taught during the following terms
Autumn Spring Summer

Module Description

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:
linear, separable.

Second-order differential equations.
reduction of order, constant coefficients;
second-order linear equations: ordinary points and regular singular points.
Euler's equation.

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


The coursework comprises 2 tests worth 10% each.

Other details

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 during Summer Examination period.

Other information

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
  • Recommended Reading:
  • 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)

Further information