Module Information

Module Identifier
MA34210
Module Title
ASYMPTOTIC METHODS IN MECHANICS
2012/2013
Co-ordinator
Semester
Semester 2
Pre-Requisite
Other Staff

Course Delivery

Delivery Type Delivery length / details
Lecture 18 lectures x 1 hour
Seminars / Tutorials 4 x 1 hours tutorials dealing with course assignments

Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   TWO HOUR EXAMINATION  100%
Supplementary Exam 2 Hours   TWO HOUR EXAMINATION  100%

Learning Outcomes

On completion of this module, a student should be able to:
1. Demonstrate an understanding of the meaning of asymptotic solutions in the appropriate context and how to interpret these;
2. Solve simple linear and nonlinear ordinary and partial differential equations by asymptotic methods;
3. Illustrate with suitable examples the occurrence of asymptotic phenomena in mechanics.

Brief description

Many mathematical problems arising in mechanics, may be formulated in terms of differential equations. However, as a rule, such problems pose new challenges from the mathematical point of view. Therefore, the simplest limit cases, which allow analytical solutions, are of particular importance. The aim of the asymptotic approach is to simplify the mathematical problem under consideration.

Content

1. Introduction to asymptotic analysis
1.1 Asymptotic expansion, Landau symbols
1.2 Main definitions and ideas, regular and singular pertubation
1.3 Singular pertubations

2. Asymptotic methods for ODE (with application to nonlinear oscillations)
2.1 Krylov-Bogoliubov averaging method
2.2 Multiple time scales method
2.3 Method of matched asymptotic expansions (MME)

3. Asymptotic methods for PDE (with application to heat/mass transfer)
3.1 Heat conduction in thin domains
3.2 Thermal constriction resistance of clusters of microcontacts (application of the MME)
3.3 Heat conduction in composites (application of the homogenization method)

Module Skills

Skills Type Skills details
Application of Number Inherent in any Mathematics module
Communication No
Improving own Learning and Performance Exposure to new area of Mathematics
Information Technology Use of computer software, including MATLAB
Personal Development and Career planning Useful addition to a student's mathematical portfolio
Problem solving Module is problem based.
Research skills Students encouraged to research additional material
Subject Specific Skills
Team work No

Notes

This module is at CQFW Level 6