2019/20 Undergraduate Module Catalogue
MATH3365 Mathematical Methods
15 creditsClass Size: 90
Module manager: Dr Stephen Griffiths
Taught: Semester 1 View Timetable
Year running 2019/20
Pre-requisite qualificationsMATH2375, or equivalent.
This module is mutually exclusive with
|MATH5366M||Advanced Mathematical Methods|
This module is not approved as a discovery module
Module summaryThis module aims to describe how precise approximations - ie ones in which the error is both understood and controllable - can be obtained using analytical (rather than numerical) techniques.
ObjectivesTo give an introduction to approximate methods of solution of ordinary and partial differential equations, and difference equations with a small parameter, since these represent the most important techniques for deriving analytical solutions when modelling real phenomena. Examples will be drawn from many areas of science and engineering.
On completion of this module, students should be armed with numerous mathematical, rather than computational, techniques for solving a wide variety of initial-value and boundary-value problems that arise in the modelling of realistic phenomena in diverse scientific areas.
In particular, students will be able to solve frequently occurring small-parameter problems using a combination of asymptotic methods such as matching, multiple scales (in space and time), and series approximations.
The governing equations of mathematical models often involve features that make it impossible to obtain their exact solution, eg the occurrence of a complicated algebraic equation; the occurrence of a complicated integral; varying coefficients in a differential equation; an awkwardly shaped boundary; a non-linear term in a differential equation.
When a large or small parameter occurs in a mathematical model of a process there are various methods of constructing perturbation expansions for the solution of the governing equations.
Often the terms in the perturbation expansions are governed by simpler equations for which exact solution techniques are available. Even if exact solutions cannot be obtained, the numerical methods used to solve the perturbation equations approximately are often easier to construct than the numerical approximation for the original governing equations.
Moreover, analytic perturbation approximations often constitute a powerful validation of any numerical model that might be employed.
- Asymptotic approximations
- Algebraic equations
- Regular perturbations in PDEs
- Boundary layers
- Matched asymptotic expansions
- Strained co-ordinates
- Multiple scales
- Accelerated convergence
- Asymptotic expansion of integrals
- Approximate solution of difference equations.
|Delivery type||Number||Length hours||Student hours|
|Private study hours||117.00|
|Total Contact hours||33.00|
|Total hours (100hr per 10 credits)||150.00|
Private studyConsolidation of course notes and background reading.
Opportunities for Formative FeedbackWeekly personal contact with lecturer in examples classes to discuss/provide assistance with regular question sheets.
Assessment of success on examples sheets.
Methods of assessment
|Exam type||Exam duration||% of formal assessment|
|Standard exam (closed essays, MCQs etc)||2 hr 30 mins||100.00|
|Total percentage (Assessment Exams)||100.00|
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Reading listThe reading list is available from the Library website
Last updated: 30/09/2019
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