Module manager: Dr Philip Walker
Email: P.Walker@leeds.ac.uk
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2012/13
MATH2365 or equivalent
| MATH2431 | Fourier Series, Partial Differential Equations and Transform |
This module is approved as an Elective
This module introduces a variety of techniques for the solution, subject to suitable boundary and initial conditions, of the basic Partial Differential Equations of mathematical physics, which describe such ubiquitous phenomena as waves and diffusion, as well as the potential problems of gravitation, electromagnetism and fluid dynamics.
On completion of this module, students should be able to:
a) obtain power series solutions of 2nd order homogeneous linear Ordinary Differential Equations;
b) test 2nd order linear differential operators for symmetry and draw appropriate conclusions from the resulting orthogonality of their eigenfunctions;
c) solve the standard Partial Differential Equations of mathematical physics in Cartesian or (2D or 3D) polar coordinates subject to given boundary conditions by the method of separation of variables, using Bessel and Legendre functions where necessary;
d) use Fourier and Laplace transforms to solve a range of boundary and initial value problems for linear Ordinary Differential Equations and Partial Differential Equations.
Separation of variables, power series solution of Ordinary Differential Equations, symmetric operators and orthogonality of eigenfunctions, Bessel and Legendre functions, their basic properties and application to boundary and initial value problems. Fourier and Laplace transforms, with applications to boundary and initial value problems.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Workshop | 10 | 1 | 10 |
| Lecture | 33 | 1 | 33 |
| Independent online learning hours | 7 | ||
| Private study hours | 100 | ||
| Total Contact hours | 43 | ||
| Total hours (100hr per 10 credits) | 150 | ||
Studying and revising of course material.
Completing of assignments and assessments.
Regular examples sheets.
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| In-course Assessment | . | 15 |
| Total percentage (Assessment Coursework) | 15 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Standard exam (closed essays, MCQs etc) | 2.0 Hrs 30 Mins | 85 |
| Total percentage (Assessment Exams) | 85 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
The reading list is available from the Library website
Last updated: 1/8/2013
Errors, omissions, failed links etc should be notified to the Catalogue Team