2020/21 Undergraduate Module Catalogue

MATH1400 Modelling with Differential Equations

10 creditsClass Size: 230

Module manager: Yue- Kin Tsang
Email: y.tsang@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2020/21

Pre-requisite qualifications

MATH1050 and (MATH1060 or MATH1331). Note that MATH1060 can be taken as a co-requisite.

This module is mutually exclusive with

LUBS1260	Mathematics for Economics and Business 1
LUBS1270	Statistics for Economics and Business 1
LUBS1280	Mathematical Economics
MATH1010	Mathematics 1
MATH1012	Mathematics 2

This module is approved as a discovery module

Module summary

The applied mathematician attempts to give a mathematical description (a mathematical model) of things in the real world. In the real world most things change with time. Mathematically a rate of change is expressed as a derivative so the applied mathematician deals mostly with equations involving derivatives - so called differential equations. This module develops the theory of differential equations and applies it to produce mathematical models describing eg 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. Students will complete a mini-project to practice presentation skills.

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 and second order differential equations to model processes such as radioactive decay, Newton cooling, population growth and mixing problems;
(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) develop communication and group working skills.

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. Reduction of order.
5. Application of second order ODEs to examples.

Teaching methods

Delivery type	Number	Length hours	Student hours
Presentation	4	1.00	4.00
Lecture	11	1.00	11.00
Tutorial	5	1.00	9.00
Private study hours			80.00
Total Contact hours			24.00
Total hours (100hr per 10 credits)			104.00

Private study

Studying and revising of course material.
Completing of assignments and assessments.

Opportunities for Formative Feedback

Regular example sheets.

!!! In order to pass the module, students must pass the examination. !!!

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
In-course Assessment	.	15.00
Project	.	5.00
Total percentage (Assessment Coursework)		20.00

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

Exams

Exam type	Exam duration	% of formal assessment
Open Book exam	2 hr 00 mins	80.00
Total percentage (Assessment Exams)		80.00

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: 21/01/2021

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