This course introduces and develops three topics that are important in applied mathematics: First order partial differential equations (PDEs) with application to traffic flow modelling, Parameter Estimation for mathematical models, and Asymptotic Analysis.
Parameter estimation and asymptotic analysis are key tools in mathematical modelling and both are associated with the parameters that arise in a model. In parameter estimation, we use methods of optimisation to find the best parameters for the model to fit data. Asymptotic analysis makes use of small or large values of parameters to find simpler expressions for mathematical models.
The course may be used as a part of a mathematics major, particularly towards the pathway in applied mathematics. It would be a useful addition to a pure mathematics or physics pathway, as well as preparation for postgraduate study in applied mathematics, pure mathematics and physics. In particular, the course is good preparation for students intending to take the partial differential equations course Maths 763 at postgraduate level. The course is useful for students who contemplate a career that involves mathematical modelling. Mathematical modelling is a key skill in physical sciences and in a diverse range of industries, including agricultural, financial, horticultural, manufacturing and energy.