## Principles of Mathematical Modelling

 Unit code: MATH20522 Credit Rating: 10 Unit level: Level 2 Teaching period(s): Semester 2 Offered by School of Mathematics Available as a free choice unit?: N

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#### 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.

#### 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.

#### Learning outcomes

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

1. Make use of the 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.

#### Assessment methods

• Other - 35%
• Written exam - 65%

#### Assessment Further Information

- written exam, 65% (1.5 hour exam)
- mid-term coursework assessment, 20%
- group poster presentation, 15% (due in week 10)

#### 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.

- 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.

#### 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.

#### Study hours

• Lectures - 22 hours
• Tutorials - 11 hours
• Independent study hours - 67 hours

#### Teaching staff

Geoffrey Evatt - Unit coordinator