Students Staff

Module Details

MA303-7-AU-CO: Ordinary Differential Equations

Note: This module is inactive. Visit the Module Directory to view modules and variants offered during the current academic year.

Year: 2018/19
Status: Inactive
Department: Mathematical Sciences
Campus: Colchester Campus
Term: Autumn
Level: Postgraduate: Level 7
Essex credit: 15
ECTS credit: 7.5
Available to Incoming Essex Abroad / Exchange students: No
Available to Outside Option: No
Available to Audit: No
Module Start and End Dates: Thursday 04 October 2018 - Friday 14 December 2018

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 Shauna McNally - Graduate Administrator. email: smcnally (Non essex users should add @essex.ac.uk to create the full email address), Tel 01206 872704

*Please note: Due to differing publication schedules, items marked with an asterisk (*) base their information upon the previous academic year.

Module Description

The module 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;
- be able to model physical systems by diffferential equations;
- be aware of the limitations of using differential equation models for real-life systems.

Teaching and Assessment

Assessment

20 per cent Coursework Mark, 80 per cent Exam Mark

Exam Duration and Period

120 minutes during Summer (Main Period) (Main)

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.

Other information

Available to Socrates /IP students spending all relevant terms at Essex.

Resources

Teaching Materials

Available via Moodle.

Lecture Recording*

No lecture recording information available for this module.

Bibliography*

This module does not appear to have a published bibliography.

Further information

Department Website: Mathematical Sciences

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