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# BSc Actuarial Science and Mathematics / Course details

Year of entry: 2021

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## Course unit details:Principles of Mathematical Modelling

Unit code MATH20522 10 Level 2 Semester 2 Department of Mathematics No

### Overview

The Principles of Mathematical Modelling course is designed to provide students with a core and implementable knowledge of how mathematics can be used at the interdisciplinary interface.

Students will attend two lectures and a problem class each week. However, every three weeks, one of those sessions will instead be a group-work task.

### Aims

• Achieve a broad understanding of the objectives of mathematical modelling within the physical sciences
• Gain a working knowledge of core techniques behind mathematical modelling
• Develop a basic ability to quantify certain phenomena associated with the physical sciences.

### Learning outcomes

On successful completion of this course unit students will be able to:

1. Make use of the SI units of dimension, and create dimensionless quantities so as to better understand physical phenomenon.
2. Use conservation equations to construct mathematical models of a range of phenomena
3. Non-dimensionalise equations and show how/when small terms can subsequently be neglected from an equation, so as to reduce their complexity.
4. Calculate the stability of 1d and 2d linear systems (and how to reduce a non-linear system down to a linear one).
5. How to communicate scientific concepts/research to a general audience.

### Syllabus

Week 1: Introduction to the mathematical modelling.
Weeks 1-3: Introduction to dimensional analysis.
Week 3-6: Introduction to conservation equations.
Weeks 7-10: Introduction to non-dimensionalisation.
Week 11: Introduction to model stability.
Week12: Revision.

### Assessment methods

Method Weight
Other 50%
Written exam 50%

Other: In class test weighting 20% and coursework weighting 30% which is a group poster exercise.

End of year examination weighting 50%.

### Feedback methods

Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

- Acheson, D. From Calculus to Chaos (Oxford, 1985) -Taylor, A. Mathematical Models in Applied Mechanics (Oxford, 1984) -Howison, S. Practical applied mathematics.

- Sonin, A. The physical basis of dimensional analysis.

### Study hours

Scheduled activity hours
Lectures 22
Tutorials 11
Independent study hours
Independent study 67

### Teaching staff

Staff member Role
Matthew Thorpe Unit coordinator
Jitesh Gajjar Unit coordinator