2009/10 Undergraduate Module Catalogue

MATH1460 Mathematics for Geophysical Sciences 1

10 Credits Class Size: 50

Module manager: Dr R. Hollerbach
Email: rh@maths.leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2009/10

Pre-requisite qualifications

A-level Mathematics

This module is approved as an Elective

Module summary

This module introduces students to basic mathematical techniques required for the physical sciences.

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) differentiate and integrate elementary functions (i.e., exponential, logarithmic, trigonometric and hyperbolic functions); b) carry out basic manipulations involving vector addition and multiplication; c) apply vector methods to simple geometrical and physical problems; d) manipulate complex numbers in Cartesian and polar form, interpret them in an Argand diagram and solve simple equations involving complex numbers; e) calculate simple limits using l'Htpital's rule where appropriate, and discuss the behaviour of a function near a limit; f) determine whether a given series converges and find the radius of convergence of a power series; g) calculate the Taylor series of a given function about a given point; h) evaluate line, surface and volume integrals using Cartesian and polar co-ordinates.

Syllabus

1. Revision of elementary functions and their inverses, differentiation and integration. Hyperbolic functions and their inverses. 2. Vector methods, including vector algebra (sums, scalar and vector products) and application to geometry (direction cosines, equations of lines, planes and spheres). Differentiation of vectors.3. Complex numbers, including De Moivre's theorem and applications; exponential formulae; roots of polynomials; the exponential, trigonometric and hyperbolic functions. 4. Limits, including l'Htpital's rule. Series. Taylor's theorem and Taylor series for one independent variable. 5. Line, surface and volume integrals using Cartesian and polar coordinates.

Teaching Methods

Methods of Assessment

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

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 website

Last updated: 22/03/2010

Errors, omissions, failed links etc should be notified to the Catalogue Team