BSc Mathematics with Finance

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 should have taken MATH11421 Introduction to ODEs or MATH11422 ODEs and Applications.

MATH11411 Introduction to Vector Calculus is recommended

• 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.

40% other assessment, of which 20% is a poster project

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.

The independent study hours will normally comprise the following. During each week of the taught part of the semester:

• You will normally have approximately 60-75 minutes of video content. Normally you would spend approximately 2-2.5 hrs per week studying this content independently
• You will normally have exercise or problem sheets, on which you might spend approximately 1.5hrs per week
• There may be other tasks assigned to you on Blackboard, for example short quizzes or short-answer formative exercises
• In some weeks you may be preparing coursework or revising for mid-semester tests

Together with the timetabled classes, you should be spending approximately 6 hours per week on this course unit.

The remaining independent study time comprises revision for and taking the end-of-semester assessment.