## MATH1460 Mathematics for Geophysical Sciences 1

### 10 creditsClass Size: 250

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

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2008/09

### 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

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Lecture 22 1.00 22.00 Tutorial 11 1.00 11.00 Private study hours 67.00 Total Contact hours 33.00 Total hours (100hr per 10 credits) 100.00

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Coursework
 Assessment type Notes % of formal assessment Tutorial Performance . 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