MA50281: Mathematical modelling for industry
[Page last updated: 23 October 2023]
| Academic Year: | 2023/24 |
| Owning Department/School: | Department of Mathematical Sciences |
| Credits: | 12 [equivalent to 24 CATS credits] |
| Notional Study Hours: | 240 |
| Level: | Masters UG & PG (FHEQ level 7) |
| Period: |
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| Assessment Summary: | CW 70%, EX 30% |
| Assessment Detail: |
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| Supplementary Assessment: |
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| Requisites: | |
| Learning Outcomes: |
* Select and apply knowledge of mathematical techniques from across a variety of mathematical sub-discipline areas to solve problems and construct an accurate approximation to the solution. * Describe limitations of the theory and the range of applications amenable to mathematical modelling. * Analyse models based on differential equations that arise in applications. * Recall and discuss approximation techniques, and apply them to relevant to industrial applications. |
| Aims: | The unit provides tools for a mathematician engaged in problem solving in a modern industrial setting. It is the first part of a bespoke package that covers the applied mathematics aspect of the training you will undergo in the course, focussing on the theoretical background. Its aim is to introduce the ideas and methods of mathematical modelling and to illustrate them with examples from industry, through a mixture of mathematical analysis and Python computing. The second part (Industrial Applications of Mathematics) will take you to concrete areas of industrial application. |
| Skills: | Mathematical model formulation, as part of the problem solving process. Solving ordinary and partial differential equations using basic asymptotic and numerical techniques. Performing programming tasks required for practical implementation of the problem-solving strategy. |
| Content: | The modelling process. Use of Python programming language. Dimensions and scaling. Basic methods for ordinary differenatial equations. Agent-based models. Asymptotic methods. Linear systems and transforms. Numerical solution of ordinary differential equations. Basic methods for partial differential equations: linear equations via Fourier Transform, wave equation, first-order nonlinear equations.
This theoretical material will be given context by applying it to concrete examples and mini case studies, such as: microwave cooking, air traffic control, crowd dynamics, undercarriage dynamics, National Grid, security scanning, wave energy, aircraft icing, demodulation, modelling industrial fires. |
| Course availability: |
MA50281 is Compulsory on the following courses:Department of Mathematical Sciences
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Notes:
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