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2023/24 Undergraduate Module Catalogue

SOEE2661 Advanced Mathematics 4

10 creditsClass Size: 50

Module manager: Dr Alex Rap

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2023/24


SOEE2041Advanced Mathematics 3

Module replaces

SOEE2660 Mathematics for Geophysical and Environmental 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 Sciences.


To provide students with sufficient Mathematical background for understanding their studies in Geophysical 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 to solve the Laplace, diffusion and wave equation in Cartesian, spherical and cylindrical polar co-ordinates employing Fourier series or other appropriate eigenfunctions;
c) obtain solutions to standard partial differential equations using Fourier transforms;
d) understand how these equations apply to relevant geophysical phenomena.


- 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.
- Fourier Transforms: Fourier sine and cosine transforms and their relationship to Fourier series.
- Complex Fourier transforms.
- Inverse transform and transform pair.
- Applications to the solution of differential equations.
- Properties - transforms of derivatives, convolution theorem.

Teaching methods

Delivery typeNumberLength hoursStudent hours
Private study hours68.00
Total Contact hours32.00
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

Example sheets are provided for students to work on independently. Assistance with these and regular informal feedback to students is given in the weekly tutorial class to continuously monitor progress. Solutions are provided after each topic is completed

Methods of assessment

Assessment typeNotes% of formal assessment
AssignmentProblem sheet - One assignment15.00
Total percentage (Assessment Coursework)15.00

Re-sits will be assessed by examination only.

Exam typeExam duration% of formal assessment
Standard exam (closed essays, MCQs etc) (S1)2 hr 00 mins85.00
Total percentage (Assessment Exams)85.00

Re-sits will be assessed by examination only.

Reading list

The reading list is available from the Library website

Last updated: 10/05/2023 16:29:07


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