MMath Mathematics and Statistics

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.

 

MATH20521 Pre-Requisites: MATH11411 and MATH11412/22

Student must have taken EITHER MATH11412 OR MATH11422.

 

• 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.

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.

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.

60% Examination

20% Group Assessment

20% Coursework

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.