"Mathematical modelling applies mathematical frameworks, such as ordinary and partial differential equations, to capture the dynamics of natural phenomena, including fluid dynamics, Newtonian and relativistic mechanics, climate, ecology, and physiology. Modelling often falls into two styles, mechanistic and phenomenological. Mechanistic modelling seeks to understand how large-scale phenomena are driven by simple, local dynamics usually governed by physical or biological laws or properties. On the other hand, phenomenological modelling seeks to capture large-scale trends of a system, such as growth, decay, and oscillations, without necessarily accounting for smaller-scale dynamics. In practice, most models combine elements of both styles. In this unit you will learn about how these mathematical frameworks are constructed and applied for particular types of phenomena which may include mathematical oncology, high Reynolds number fluid flow, stellar atmosphere, terrestrial climates, populations of cells or organisms or other areas of mathematical interest. You will analyse both classical and new models and critique their applicability and use their predictions to explore aspects of the natural world. Inspired by these ideas, you will have the opportunity to create new models in tutorials and assignments and to use them to solve complex mathematical and scientific problems. By doing this unit, you will learn how mathematics is applied in both simple and complicated models and explore the ways that mathematical analysis creates insight into natural phenomena. "
4 contact hours/week comprising lectures, and tutorials or seminars
tutorial participation (10%), assignments (40%), final exam (50%)
Familiarity with the modelling and analysis using differential equations (e.g., MATH3063, MATH4063, MATH3078, MATH4078 or MATH4074) and the ability to write code and numerical schemes to solve standard applied mathematical problems (e.g., MATH4076 or MATH3076 or MATH4411 or equivalent). Please consult with the coordinator for further information.