Nonlinear Systems and Applications - MA6544

Location Term Level Credits (ECTS) Current Convenor 2017-18 2018-19
Canterbury Autumn
View Timetable
6 15 (7.5) PROF PA Clarkson

Pre-requisites

None

Restrictions

None

2017-18

Overview

This module will give an introduction to nonlinear ordinary differential equations and difference equations. Such ordinary differential equations and difference equations have a variety of applications such as Mathematical Biology and Ecology.   The emphasis will be on developing an understanding of ordinary differential equations and difference equations and using analytical and computational techniques to analyse them. Topics include: phase plane, equilibria and stability analysis; periodic solutions and limit cycles; Poincare-Bendixson theorem; dynamics of difference equations: cobwebs, equilibria, stability and periodic solutions; the discrete logistic model and chaos.   The material is chosen so as to demonstrate the range of modern analytical and computational techniques available for solving nonlinear ordinary differential equations and difference equations and to illustrate the many different applications which are modelled by such equations. A range of Mathematical tools are drawn together to study the nonlinear equations, including computation through the use of MAPLE.

Details

Contact hours

42

Method of assessment

80% examination, 20% coursework

Preliminary reading

Jordan, J. W., and Simth, P., Nonlinear Ordinary Differential Equations: an introduction for scientists and engineers, Oxford University Press, Fourth Edition, 2007
Elaydi, S., An introduction to difference equations, Springer, 1999
Murray, J. D., Mathematical Biology I: An Introduction, Springer, Third Edition, 2002
Glendinning, P. A., Stability, Instability and Chaos: An Introduction to the Qualitative Theory of Differential Equations, Cambridge University Press, 1994
Kaplan, D., and Glass, L., Understanding Nonlinear Dynamics, Springer, 1995

See the library reading list for this module (Canterbury)

See the library reading list for this module (Medway)

Learning outcomes

On successfully completing the level 6 module students will be able to:
1 demonstrate systematic understanding of key aspects of introductory nonlinear systems;
2 demonstrate the capability to deploy established approaches accurately to analyse and solve problems using a reasonable level of skill in calculation and manipulation of the material in the following areas: equilibra for both nonlinear differential and difference equations and their stability, phase portraits, the existence of limit cycles;
3 apply key aspects of nonlinear systems in well-defined contexts, showing judgement in the selection and application of tools and techniques;
4 show judgement in the selection and application of Maple.

The intended generic learning outcomes.
On successfully completing the level 6 module students will be able to:
1 manage their own learning and make use of appropriate resources;
2 understand logical arguments, identifying the assumptions made and the conclusions drawn;
3 communicate straightforward arguments and conclusions reasonably accurately and clearly;
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
5 solve problems relating to qualitative and quantitative information;
6 make competent use of information technology skills such online resources (Moodle), internet communication;
7 communicate technical material competently;
8 demonstrate an increased level of skill in numeracy and computation;
9 demonstrate the acquisition of the study skills needed for continuing professional development.

University of Kent makes every effort to ensure that module information is accurate for the relevant academic session and to provide educational services as described. However, courses, services and other matters may be subject to change. Please read our full disclaimer.