This module will present examples of mathematical models arising from practical problems in technological settings. For each case study, all stages of modelling will be discussed, including model formulation, mathematical analysis, numerical simulation and visualization of solutions. It aims to introduce and familiarize students with mathematical research which is problem oriented instead of topic oriented; to give students experience with formulating and analysing mathematical models.
The process of mathematical modelling: Scaling techniques and non-dimensionalization; Physical conservation laws.
A short introduction to Asymptotic methods.
A short introduction to dynamical systems methods.
Problem solving through case studies.
Extensive problem solving sessions supported by lectures presenting relevant material and use of a mathematical software package (MAPLE/R).
|Module Content & Assessment