2008/09 Undergraduate Module Catalogue
MATH2450 Mathematics for Geophysical Sciences 3
10 creditsClass Size: 200
Module manager: Professor J.H. Merkin
Email: amtjhm@maths.leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2008/09
Pre-requisites
| MATH1150 | Mathematics for Geophysical Sciences 2 |
| MATH1460 | Mathematics for Geophysical Sciences 1 |
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;
e) solve standard second order PDEs by separation of variables.
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. Partial Differential Equations: Second order PDEs. Laplace's equations, diffusion equations, wave equation. Solution by separation of variables. Applications to include heat flow in a rod and waves on strings.
Teaching methods
| Delivery type | Number | Length hours | Student hours |
| Example Class | 11 | 1.00 | 11.00 |
| Lecture | 22 | 1.00 | 22.00 |
| Private study hours | 67.00 | ||
| Total Contact hours | 33.00 | ||
| Total hours (100hr per 10 credits) | 100.00 | ||
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 | 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: 27/04/2009
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