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Module Title
LI Differential Equations
School
Mathematics
Department
Mathematics
Module Code
06 25670
Module Lead
Dr Chris Good
Level
Intermediate Level
Credits
20
Semester
Semester 2
Pre-requisites
Co-requisites
Restrictions
None
Exclusions
Description
When mathematical modelling is used to describe physical, biological, chemical or other phenomena, one of the most common results is either a differential equation or a system of differential equations, which, together with appropriate boundary and/or initial conditions, describe the situation. These differential equations can be either ordinary (ODEs) or partial (PDEs) and finding and interpreting their solution lies at the heart of applied mathematics. This module develops the theory of differential equations with a particular focus on techniques of solving both linear and nonlinear ODEs. Fourier series, which arise in the representation of periodic functions, and special functions, which arise in the solution of PDEs such as Laplace’s equation that models the flow of potential, are also introduced. A number of the classical equations of mathematical physics are solved.
Learning Outcomes
By the end of the module students should be able to:
use phase-plane methods to analyse second order nonlinear ordinary differential equations
formulate and analyse the equations of motion for particles under the action of applied forces
set up boundary value problems for ordinary differential equations using a variety of techniques
solve various linear and nonlinear ODEs using a variety of techniques
calculate the Fourier series of a function and recognise when the series converges to the function
Assessment
25670-01 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions
3 hour Written Unseen Examination (80%); In-course Assessment (20%).
