MATH2450 Mathematics for Geophysical Sciences 3

10 creditsClass Size: 30

Module manager: Dr G Lythe
Email: grant@maths.leeds.ac.uk

Taught: Semester 1 View Timetable

Year running 2011/12

Pre-requisites

 SOEE1301 Intermediate Mathematics for Environmental and Geophysical S SOEE1311 Advanced Mathematics for Environmental and Geophysical Scien

This module is mutually exclusive with

 MATH1060 Introductory Linear Algebra MATH2365 Vector Calculus MATH2420 Multiple Integrals and Vector Calculus

This module is approved as an Elective

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 Sciences.

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 Workshop 10 1.00 10.00 Lecture 22 1.00 22.00 Private study hours 68.00 Total Contact hours 32.00 Total hours (100hr per 10 credits) 100.00

Opportunities for Formative Feedback

Regular problem solving assignments

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 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