2008/09 Undergraduate Module Catalogue

MATH1400 Modelling with Differential Equations

10 creditsClass Size: 250

Module manager: Professor A. Rucklidge
Email: a.m.rucklidge@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2008/09

Pre-requisite qualifications

A good A-level Mathematics grade or equivalent.

This module is mutually exclusive with

MATH1932	Calculus, ODEs and Several-Variable Calculus
MATH1970	Differential Equations

This module is approved as an Elective

Module summary

This module develops the theory of differential equations and applies it to produce mathematical models describing e.g. the way in which the population of the world varies with time, and the way in which an influenza virus propagates through a university campus.

Objectives

To introduce the concept of mathematical modelling. To illustrate its application in various areas and to develop relevant methods for the solution of first and second order ODEs. On completion of this module, students should be able to: (a) set up simple first order differential equations to model processes such as radioactive decay and Newton cooling; (b) solve first order differential equations of various types such as separable, homogenous, linear, and to apply initial conditions to the general solution; (c) solve second order linear differential equations with constant coefficients by finding complementary functions and particular integrals, and to apply either initial or boundary conditions; (d) linearise systems of first order differential equations, find their equilibrium points, and classify the equilibrium points of systems of two variables; (e) apply the phase plane method to physical systems of two variables, such as the predator-prey model.

Syllabus

1. The modelling process via simple examples: exponential growth and decay etc. 2. Solution of first order ODEs: linear via integrating factor, nonlinear via substitutions. 3. Application of first order ODEs to modelling population growth, etc. 4. Solution of second order ODEs (linear with constant coefficients) and simultaneous ODEs. 5. Application of second order ODEs to interacting population models etc. 6. Partial differentiation, classification of critical points of two-variable functions. 7. Introduction to phase plane methods: critical points, node, saddle, focus, centre.

Teaching methods

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

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

Reading list

The reading list is available from the Library website

Last updated: 31/03/2009

Disclaimer

Browse Other Catalogues

• Undergraduate module catalogue
• Taught Postgraduate module catalogue
• Undergraduate programme catalogue
• Taught Postgraduate programme catalogue

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