Mathematical modelling B
BS BT DT BC BP BDT
Dr Alistair Carr
6 points * Second semester * 4 hours per week * Gippsland/Distance (odd-numbered years only) * Prerequisites: GAS1612, GAS1621, GAS2612; and GCO1811, or GCO1832 or 7221 - offered pre-1992, (GAS1631, GAS2622 are desirable)
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
Prescribed texts
Beltrami E Mathematics for dynamic modeling Academic Press, 1987
Kapur J N Mathematical modelling Wiley, 1988
Recommended texts
Devaney R L A first course in chaotic dynamical systems: Theory and experiment Addison-Wesley, 1992
Dym C and Ivey E Principles of mathematical modeling Academic Press, 1980
Pottage J Geometrical investigations: Illustrating the art of discovery in the mathematical field Addison-Wesley, 1983
Saaty T and Alexander J Thinking with models Pergamon, 1981