Engineering Mathematics Brochure: Course profiles

Nonlinear Dynamics and Chaos

This course is taught in year three of the Engineering Mathematics programme, and is also taken as an option by many other students from the Faculty of Engineering, from Physics and from Mathematics. Nonlinear Dynamics & Chaos is consistently rated as one of the most popular courses in the Faculty. It is currently taught by Hinke Osinga, Reader in Mathematics.

But what is this course about?

It is about chaotic behaviour in seemingly quite simple systems. Chaos is effectively unpredictable long time behavior arising in a deterministic dynamical system because of sensitivity to initial conditions. Chaotic motion is often considered a bad thing in engineering because it can lead to catastrophic failure, for example in the famous collapse of the Tacoma Narrows bridge. On the other hand, chaos is desirable in a wide variety of situations, such as mixing processes in the food, pharmaceutical and process industries, or for the rapid suppression of heart attacks. Chaotic behaviour is associated with intriguing geometrical objects, such as the ones shown on the poster (various views of which are shown in the four images below) on the front page and on the chaotic laser light page.

The course will teach you the basic concepts and methods to find, understand and appreciate complicated behaviour in engineering systems. If you still want to know more afterwards, we offer a follow-on course Advanced Nonlinear Dynamics & Chaos...

     

Computational Intelligence

For computer systems to be able to reason intelligently, they must have a suitable framework for representing their knowledge about the world. If a robot is to perform its tasks successfully, it must have knowledge of its environment. This includes the position of objects and boundaries and more general knowledge such as physical laws, which must be represented in a formal mathematical way. This presents us with a challenge: most knowledge about the real world is imprecise and uncertain whereas traditional mathematical frameworks are characterised by precision and certainty.

Uncertainty Modelling is a fourth year course, currently taught by Jonathan Lawry, Professor of Artificial Intelligence. It introduces formal frameworks that permit representation of imprecise and uncertain knowledge, allowing for reasoning to infer new information from available knowledge. This reasoning with uncertainty can be applied to logical systems based on either numbers, or words and relationships. Mathematical ways of modelling imprecise and vague concepts such as high, low and approximately equal are also introduced. This reasoning with uncertainty can be applied to logical systems based either on numbers, or words and relationships.

Case Studies

A particular feature of the second year is the Case Studies course, one in the modelling theme that runs through all four years. Students work in groups of three or four on technological problems, often derived from actual industrial situations and presented in a "real life" format. Each group has frequent discussions with a member of staff who plays the role of an industrial manager. Typically, each Case Study lasts two or three weeks, and is an opportunity to use the techniques and theory taught in other courses.

Examples of case study activities

• Modelling water levels in a hydroelectric dam system
• Development of a digital television system
• Modelling blood sugar levels in patients with diabetes
• Estimation of the power requirement for the drive motor in a radar system
• Investigation of bearing erosion in diesel engines

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