2016/17 Undergraduate Module Catalogue

SOEE2660 Mathematics for Geophysical and Environmental Sciences 4

10 creditsClass Size: 50

Module manager: Prof Greg Houseman
Email: G.A.Houseman@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2016/17

Pre-requisites

MATH2450

Mathematics for Geophysical Sciences 3

Module replaces

MATH2490 Mathematics for Geophysical Sciences 4

This module is not approved as a discovery module

Module summary

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

Objectives

To provide students with sufficient Mathematical background for understanding their studies in Geophysical and Atmospheric Sciences.

Learning outcomes
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

- Partial Differential Equations: Laplace's equation, diffusion equation, wave equation.
- Separation of variables in cylindrical and spherical co-ordinates.
- 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.
- Point source solution and Green's function.
- 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
Lecture	22	1.00	22.00
Practical	10	1.00	10.00
Private study hours			68.00
Total Contact hours			32.00
Total hours (100hr per 10 credits)			100.00

Private study

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

Opportunities for Formative Feedback

Regular informal feedback to students in weekly example class to continuously monitor progress.
Written feedback at the end of the semester from the assessed example questions.

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
Practical	Weekly example worksheets	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 00 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: 11/01/2017

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