## MA4AM-Asymptotic Methods

Module Provider: Mathematics and Statistics
Number of credits: 20 [10 ECTS credits]
Level:7
Terms in which taught: Autumn / Spring term module
Pre-requisites: MA2ODE Ordinary Differential Equations and MA2PDE Partial Differential Equations
Non-modular pre-requisites:
Co-requisites:
Modules excluded: MA3AM Asymptotic Methods
Module version for: 2017/8

Module Convenor: Prof Paul Glaister

Summary module description:
Foremost among the analytic techniques used in applications are the systematic methods of perturbations (asymptotic expansions) in terms of a small or large parameter or co-ordinate. This module is concerned with perturbation methods and applications will be made to non-linear equations, integrals and some ordinary differential equations.

Aims:
To introduce the basic ideas of asymptotic analysis and the development of skills in solving a range of problems, mainly involving non-linear equations, integrals and differential equations.

Assessable learning outcomes:

By the end of the module students are expected to be able to:

• construct and use uniform asymptotic expansions for a range of appropriate problems, including non-linear equations, integrals and differential equations.

This module will be assessed to a greater depth than the excluded module MA3AM.

Outline content:
Foremost among the analytic techniques used in applications are the systematic methods of perturbations (asymptotic expansions) in terms of a small or large parameter or co-ordinate. This module is concerned with perturbation methods and applictions will be made to non-linear equations, integrals and some ordinary differential equations.

Brief description of teaching and learning methods:
Lectures supported by problem sheets.

Contact hours:
 Autumn Spring Summer Lectures 20 20 Guided independent study 80 80 Total hours by term 100.00 100.00 Total hours for module 200.00

Summative Assessment Methods:
 Method Percentage Written exam 100

Other information on summative assessment:
One examination paper.

Formative assessment methods:
Problem sheets.

Penalties for late submission:
The Module Convenor will apply the following penalties for work submitted late, in accordance with the University policy.

• where the piece of work is submitted up to one calendar week after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for the piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

• The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Length of examination:
3 hours.

Requirements for a pass:

A mark of 50% overall.

Reassessment arrangements:
One examination paper of 3 hours duration in August/September.