# 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
Co-requisites:

Staff
Supervisor: Dr Georgi Grahovski
Teaching Staff: Dr Georgi Grahovski, email grah@essex.ac.uk; Prof Edd Codling, email ecodling@essex.ac.uk
Contact details: Miss Claire Watts, Department Manager. email: cmwatts@essex.ac.uk, 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.

Syllabus:
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.

### Assessment

20 per cent Coursework Mark, 80 per cent Exam Mark

### Coursework

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.