2008/09 Undergraduate Module Catalogue

MATH2490 Mathematics for Geophysical Sciences 4

10 creditsClass Size: 200

Module manager: Dr P Crompton
Email: crompton@maths.leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2008/09

Pre-requisites

MATH2450

Mathematics for Geophysical Sciences 3

This module is approved as an Elective

Module summary

This module introduces students to the mathematical techniques required to solve differential equations arising in the Geophysical sciences.

Objectives

To provide students with sufficient Mathematical background for understanding their studies in Geophysical Sciences.
On completion of this module, students should be able to:

a) solve ordinary differential equations using series solutions, obtain properties of these solutions and relationships between them;
b) use separation of variables combined with either Fourier series or Fourier transforms to solve the Laplace, diffusion and wave equation in Cartesian, spherical and cylindrical polar co-ordinates;
c) obtain the Fourier transforms of simple functions; solve simple ordinary differential equations using Fourier transforms.

Syllabus

Ordinary Differential Equations: Introduction to Sturm-Liouville theory - eigenvalues, eigenfunctions, differential operators, orthogonality. Series solutions of ODEs - Frobenius' method. Legendre's equations and Legendre polynomials. Bessel's equations. Generating functions and recurrence relations. Partial Differential Equations: Laplace's equation, diffusion equation, wave equation. Point source solution and Green's function. Separation of variables in cylindrical and spherical co-ordinates.. Fourier Transforms: Fourier sine and cosine transforms and their relationship to Fourier series. Relationship to discrete Fourier transforms. Complex Fourier transforms. Inverse transform and transform pair. Applications to the solution of differential equations. The uncertainty principle. Properties - transforms of derivatives, convolution theorem, transfer functions..

Teaching methods

Delivery type	Number	Length hours	Student hours
Example Class	11	1.00	11.00
Lecture	22	1.00	22.00
Private study hours			67.00
Total Contact hours			33.00
Total hours (100hr per 10 credits)			100.00

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	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: 31/03/2009

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