# 2023/24 Undergraduate Module Catalogue

## SOEE2041 Advanced Mathematics 3

### 10 creditsClass Size: 50

**Module manager:** Dr Alex Rap**Email:** a.rap@leeds.ac.uk

**Taught:** Semester 1 (Sep to Jan) View Timetable

**Year running** 2023/24

### Pre-requisites

SOEE1302 | Advanced Mathematics 1 |

SOEE1312 | Advanced Mathematics 2 |

Module replaces

SOEE2040 Mathematics for Geophysical and Environmental Sciences 3**This module is not approved as a discovery module**

### Module summary

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 of geophysics such as fluid flow and heat transfer.### Objectives

To provide the 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) carry out basic manipulations involving determinants and matrices;

b) find eigenvalues and eigenvectors of given matrices;

c) calculate the gradient of a scalar field and the divergence and curl of a vector field;

d) evaluate line, surface and volume integrals using Cartesian and polar co-ordinates.

### Syllabus

- 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.

### Teaching methods

Delivery type | Number | Length hours | Student hours |

Lecture | 20 | 1.00 | 20.00 |

Tutorial | 10 | 1.00 | 10.00 |

Private study hours | 70.00 | ||

Total Contact hours | 30.00 | ||

Total hours (100hr per 10 credits) | 100.00 |

### Private study

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

### Opportunities for Formative Feedback

Regular problem solving assignments### Methods of assessment

**Coursework**

Assessment type | Notes | % of formal assessment |

Assignment | Problem Sheet - One Assignment | 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) (S1) | 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 websiteLast updated: 10/05/2023 16:29:07

## Browse Other Catalogues

- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue

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