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MAT-20041 - Module Specification
School of Computer Science and Mathematics
Faculty of Natural Sciences

For academic year: 2026/27 Last Updated: 17 March 2026

MAT-20041 - Linear Differential Equations
Coordinator: Liudmila Prikazchikova Tel: +44 1782 7 34779
Lecture Time: See Timetable...
Level: Level 5
Credits: 15
Study Hours: 150
School Office: 01782 733075

Programme/Approved Electives for 2026/27

None

Available as a Free Standing Elective

No

Co-requisites

None

Prerequisites

MAT-10075 Differential Equations and Multivariable Calculus

Barred Combinations

None

Description for 2026/27

Differential equations are used as mathematical models describing various processes in the real world. This helps us investigate problems related to population dynamics, heat dissipation in objects, vibrations of engineering structures and wave propagation, among many others. Some situations require more than one differential equation to be solved at once, e.g., modelling dynamics of two populations (e.g., foxes and rabbits). Within this module we will study a variety of methods for solving differential equations.

Aims
This module aims to further develop skills and mathematical techniques, with a particular focus on methods for solving linear ordinary differential equations (ODEs). An introduction to phase plane analysis of nonlinear systems, as well as some basic techniques for solving partial differential equations (PDEs) will also be provided.

Intended Learning Outcomes

analyse a differential equation, then select and apply appropriate theoretical material and/or computational methods to solve the equation: 1,3
interpret the behaviour of solutions of differential equations through the use of phase-plane analysis: 2,3
apply Laplace integral transform to solution of initial value problems for linear differential equations: 3

Study hours

Lectures: 36 hours
Tutorials: 12 hours
Preparation to assessment: 12 hours
Independent study: 90 hours

School Rules

None

Description of Module Assessment

1: Problem Sheets weighted 15%
Problem Sheets
A set of 5 problem sheets with short questions. The mark in this assessment will be constituted by 3 best marks out of 5.

2: Class Test weighted 15%
Class test
40 min class test covering mainly phase-plane analysis

3: Exam weighted 70%
Final exam (2 hours)
The examination paper will consist of no less than five and not more than eight questions all of which are compulsory.

The University undertakes a continuous review of its teaching and research provision to ensure programmes are of a high quality and changes may be made to modules where it is necessary and reasonable to do so. Please be aware that minor changes to modules, such as a change to an individual assessment, can occur up until enrolment, although we endeavour to give you as much notice as possible of any changes. Details about the circumstance in which changes are made to programmes can be found in the Student Agreement, available at: https://www.keele.ac.uk/legalgovernancecompliance/governance/actcharterstatutesordinancesandregulations/studenttermsconditions/

Last Updated: 17 March 2026