Gwybodaeth Modiwlau
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
1.1 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