2014/15 Undergraduate Module Catalogue

MATH2375 Linear Differential Equations and Transforms

15 creditsClass Size: 240

Module manager: Prof Allan Fordy
Email: A.P.Fordy@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2014/15

Pre-requisite qualifications

MATH2365 or equivalent

This module is mutually exclusive with

MATH2431

Fourier Series, Partial Differential Equations and Transform

This module is approved as a discovery module

Module summary

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.

Objectives

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.

Syllabus

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.

Teaching methods

Delivery type	Number	Length hours	Student hours
Workshop	10	1.00	10.00
Lecture	33	1.00	33.00
Independent online learning hours			7.00
Private study hours			100.00
Total Contact hours			43.00
Total hours (100hr per 10 credits)			150.00

Private study

Studying and revising of course material.
Completing of assignments and assessments.

Opportunities for Formative Feedback

Regular examples sheets.

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
In-course Assessment	.	15.00
Total percentage (Assessment Coursework)		15.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 30 mins	85.00
Total percentage (Assessment Exams)		85.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 02/02/2015

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