Authorised by Academic Registrar, April 1996
Objectives For students to develop a broader understanding of the modelling process and its place in applying mathematics; to understand key features of modern dynamical systems theory at an elementary level, including such concepts as stability analysis, linearisation, asymptotic stability, birfurcation, limit cycles, strange attractors and chaotic solutions; to be able to apply these ideas and associated analytical methods to simple models drawn from the physical and biological sciences.
Synopsis This subject is intended to extend the student's knowledge of, and skill in, mathematical modelling techniques, beyond the introduction provided in subjects GAS1621 and GAS2062/2064. We introduce several techniques of classical and modern applied mathematics, particularly for case studies in the behaviour of dynamical systems. Mathematical discovery and analysis; questions of representation, reductionism, precision, generality and fertility in modelling; styles of modelling, eg empirical versus theoretical, discrete versus continuous, stochastic versus deterministic; sub-models and global models; modelling using - conservation laws, criteria for stability, asymptotic approximations, differential equations, numerical approximation, estimation, and physical conditions; introduction to modelling dynamical systems including uniqueness, stability, linearisation, cycles and bifurcation, catastrophe, chaotic behaviour, simulation.
Assessment Three assessment assignments: 70% + One two-hour examination: 30% + Students must pass both the assignment work and the examination in order to receive a passing grade