- Dr Andrew Hazel (Reader - University of Manchester)
|Delivery Type||Delivery length / details|
|Lecture||22 x 1 Hour Lectures|
|Assessment Type||Assessment length / details||Proportion|
|Semester Exam||2 Hours (Written Examination)||100%|
|Supplementary Exam||2 Hours (Written Examination)||100%|
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.
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.
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.
|Skills Type||Skills details|
|Application of Number||Inherent in any Mathematics module|
|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|
This module is at CQFW Level 6