# Gwybodaeth Modiwlau

Module Identifier
MA34210
Module Title
Asymptotic Methods in Mechanics
2019/2020
Co-ordinator
Semester
Semester 2
Pre-Requisite
External Examiners
• Dr Andrew Hazel (Reader - University of Manchester)

Other Staff

#### Course Delivery

Delivery Type Delivery length / details
Lecture 22 x 1 Hour Lectures

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   (Written Examination)  100%
Supplementary Exam 2 Hours   (Written 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. Fundamentals: main ideas and techniques, definitions of Landau symbols, asymptotic sequences and series.
2. Regular perturbation methods: polynomials, ordinary differential equations.
3. Singular perturbation methods: dominant balance, Kruskal-Newton graphs.
4. Asymptotic approximation of integrals: Taylor series, Laplace's method.
5. Non-linear oscillations: physical motivation, Duffing equation, secular terms, Linstedt-Poincare method.
6. Damped oscillations: physical motivation, two-scale method.
7. Method of matched asymptotics: techniques and application.
8. Heat conduction in thin domains.

### 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