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Unit information: Mathematics of Movement in 2022/23

Please note: you are viewing unit and programme information for a past academic year. Please see the current academic year for up to date information.

Unit name Mathematics of Movement
Unit code EMATM0064
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 1 (weeks 1 - 12)
Unit director Professor. Giuggioli
Open unit status Not open
Units you must take before you take this one (pre-requisite units)

EMAT33100 or alternative unit(s) where students have been exposed to Laplace and Fourier transforms and analytical solutions of partial differential equations. It is imperative that students have learnt how to use Laplace and Fourier transforms, how to solve analytically partial differential equations and have familiarity with probability concepts.

Units you must take alongside this one (co-requisite units)

none

Units you may not take alongside this one

none

School/department School of Engineering Mathematics and Technology
Faculty Faculty of Engineering

Unit Information

This unit teaches how to represent mathematically in space and time an object or entity that moves randomly, e.g. a robot searching for its targets, an animal foraging, or a human roaming inside a mall. The formalisms that the unit cover include continuous space and time variables, discrete space and time variables, and discrete space and continuous time variables. The knowledge gained from this unit has applications to the vast number of technologies that track the displacement of mechanical or biological entities, from GPS and RFID recordings to video images. More broadly this unit equip students with the necessary mathematical techniques to describe the dynamics of a random or stochastic system.

Your learning on this unit

By the end of this unit, you will be able to use appropriate tools to study the spatio-temporal dynamics of a randomly moving entity. Specifically, you will know how to:

  1. Write the most appropriate quantitative representation (discrete or continuous variables) to describe random motion in finite and infinite space, both via stochastic differential equations or probability equations.
  2. Use techniques to solve stochastic differential equations and discrete or continuous partial differential equations.
  3. Use concepts such as the first-passage time and first-encounter time to characterise the statistics of the random movement of one or multiple entities.

How you will learn

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.

How you will be assessed

Tasks which help you learn and prepare you for summative tasks (formative):

Students will be given an in class formative test half way through the unit to help them in their learning of the material taught till then. Students will receive feedback by going through the correct test solutions with the lecturer at the end of the class test.

Tasks which count towards your unit mark (summative):

There will be one summative exam which counts 100% towards the final mark. This exam will assess all ILOs.

When assessment does not go to plan

For the re-assessment students will need to pass another exam style assessment where they demonstrate achievement of the learning outcomes covered by the original assessment.

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. EMATM0064).

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.

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