Module manager: Jonathon Mound
Email: J.E.Mound@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2026/27
| SOEE1302 | Advanced Mathematics 1 |
| SOEE1312 | Advanced Mathematics 2 |
SOEE2040 Mathematics for Geophysical and Environmental Sciences 3
This module is not approved as a discovery module
The topics covered in this module are essential mathematical tools for treating many physical phenomena. Matrices provide a powerful tool for storing, displaying and manipulating information about linear systems of algebraic and differential equations. They are, for example, used extensively in the analysis of vibrating systems such as those encountered in seismology. The operations of differentiating and integrating scalar and vector fields arise naturally in areas such as fluid flow and heat transfer. The geometry of natural systems means that the equations describing their behaviour may be best described in non-Cartesian coordinates.
This module will provide the students with sufficient Mathematical background for understanding their studies in Atmospheric, Environmental, Geographic, and Geophysical Sciences. Lectures will introduce the mathematical techniques and demonstrate examples of use. Tutorials will encourage practice and give feedback enabling students to build skill. Assessment will provide the opportunity to demonstrate understanding, problem solving, and critical ability.
On successful completion of the module students will have demonstrated the following learning outcomes relevant to the subject:
SSLO1: carry out manipulations involving determinants and matrices;
SSLO2: find eigenvalues and eigenvectors of given matrices;
SSLO3: calculate the gradient and Laplacian of a scalar field and the divergence and curl of a vector field in Cartesian, cylindrical, and spherical coordinates;
SSLO4: evaluate line, surface, and volume integrals using Cartesian, cylindrical, and spherical co-ordinates.
On successful completion of the module students will have demonstrated the following skills learning outcomes:
SKLO1: Problem solving & analytical skills: take an effective approach to solving problems using both analytical and creative skills;
SKLO2: Critical thinking: evaluate information and arguments, using supporting evidence to assess arguments, theories, and ideas;
SKLO3: Subject specific technical skills: recognise and use subject-specific theories, paradigms, concepts, and principles in the fields of matrix algebra and vector calculus.
- Determinants and Matrices: Determinants and solution of linear equations.
- Basic matrix algebra.
- Transpose and inverse of a matrix.
- Symmetric, orthogonal and Hermitian matrices.
- Eigenvalues and eigenvectors: rotation of co-ordinate axes.
- Diagonalisation of real symmetric matrices; quadratic forms.
- Vector Calculus: Gradient, divergence and curl.
- Second order derivatives; the Laplacian; vector identities.
- Expressions in spherical polar co-ordinates.
- Line, surface and volume integrals involving vector fields.
- Flux and the divergence theorem; Circulation and Stokes' theorem.
- Laplace's equation, diffusion equation.
- Solution by separation of variables.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Practicals | 10 | 1 | 10 |
| Lecture | 20 | 1 | 20 |
| Private study hours | 70 | ||
| Total Contact hours | 30 | ||
| Total hours (100hr per 10 credits) | 100 | ||
Completing of assignments for workshops and assessments.
Studying and revising of course material.
Regular problem solving assignments
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| Coursework | Coursework | 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) (S1) | 2.0 Hrs 0 Mins | 85 |
| Total percentage (Assessment Exams) | 85 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Check the module area in Minerva for your reading list
Last updated: 30/04/2026
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