Unit information: Delay and stochastic equations in engineering and biology in 2021/22

Unit name	Delay and stochastic equations in engineering and biology
Unit code	EMATM0024
Credit points	10
Level of study	M/7
Teaching block(s)	Teaching Block 1 (weeks 1 - 12)
Unit director	Professor. John Hogan
Open unit status	Not open
Pre-requisites	EMAT33100, or an alternative (including Laplace transforms)
Co-requisites	none
School/department	Department of Engineering Mathematics
Faculty	Faculty of Engineering

Description including Unit Aims

This unit covers the theory and application of two important types of equations that occur widely in engineering and biology. Delay equations occur when the dynamics of a system depends on the state of the system at a past time. For example, almost any control system has delays in it due the time taken for measurement and processing. Delay equations are infinite dimensional systems that require careful solution and interpretation. Stochastic equations occur whenever there is noise in a system. Brownian motion is the most widely known example, and all of modern financial mathematics is based on these equations.

Intended Learning Outcomes

By the end of this unit, you will be able to use appropriate tools to analyse systems with either delays or stochastic effects. Specifically, you will know how to:

1. Solve simple linear delay equations using Laplace transforms and see if the solution is stable or not.
2. Solve simple stochastic equations and understand concepts such as the first passage time and the time evolution of the probability density function.
3. Numerically solve nonlinear delay or nonlinear stochastic equations using appropriate methods.

Teaching Information

Teaching will be delivered through a combination of synchronous and asynchronous sessions, including lectures, supported by live online sessions, problem sheets and self-directed exercises.

Assessment Information

1 Summative Assessment, 100% - Exam. This will assess all ILOs.

Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. EMATM0024).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the Faculty workload statement relating to this unit for more information.

Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).
The Board of Examiners will take into account any extenuating circumstances and operates within the Regulations and Code of Practice for Taught Programmes.