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2009/10 Undergraduate Module Catalogue

MATH1150 Mathematics for Geophysical Sciences 2

10 creditsClass Size: 50

Module manager: Dr M. Ivanchenko
Email: m.ivanchenko@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2009/10

Pre-requisite qualifications

A good A-level Mathematics grade or equivalent.

This module is mutually exclusive with

MATH1400Modelling with Differential Equations
MATH1410Modelling Force and Motion
MATH1970Differential Equations
MATH2365Vector Calculus

This module is approved as an Elective

Module summary

This module introduces students to basic techniques of Mathematics required for the geophysical sciences such as functions of several variables, ordinary differential equations, Fourier series, introduction to linear systems.

Objectives

On completion of this module, students should be able to:
a) calculate partial derivatives of explicitly and implicitly defined functions and use the chain rule;
b) calculate the Taylor series of a given function of two variables about a given point;
c) find and classify critical points of a function of two variables;
d) solve simple first order ordinary differential equations and linear second order ordinary differential equations;
e) determine whether a function is periodic and calculate its Fourier series;
f) solve simple linear problems using Laplace transforms.

Syllabus

1. Functions of Several Variables, examples, visualisation by graphs or contours, limits and continuity. Partial derivatives, meaning and calculation, higher derivatives. Chain rule and applications. Taylor series in two variables. Maxima and minima of functions of two or more variables.
2. Ordinary Differential Equations, examples and definitions. Solution of first order ODEs, including separation of variables, integrating factors for linear ODEs, homogeneous equations and exact differentials. Solution of second order linear equations with constant coefficients.
3. Fourier Series, examples and formulae. Even and odd functions, half range series, complex form of a Fourier series. Formulae for arbitrary periods. Applications to vibrating strings.
4. Linear systems. Response of linear system to harmonic input. Example of the seismometer. Solution of linear problems by Laplace transform. Transfer function.

Teaching methods

Delivery typeNumberLength hoursStudent hours
Lecture221.0022.00
Tutorial111.0011.00
Private study hours67.00
Total Contact hours33.00
Total hours (100hr per 10 credits)100.00

Methods of assessment


Coursework
Assessment typeNotes% 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 typeExam duration% of formal assessment
Standard exam (closed essays, MCQs etc)2 hr 00 mins85.00
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 website

Last updated: 22/03/2010

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