Mathematical modelling B
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)
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 GAS2624. We introduce several techniques of classical and modern applied mathematics, particularly for case studies in the behaviour of continuous or discrete dynamical systems; and concepts and techniques such as 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
Devaney R L A first course in chaotic dynamical systems: Theory and experiment Addison-Wesley, 1992
Kapur J N Mathematical modelling Wiley, 1988
Recommended texts
Saaty T and Alexander J Thinking with models Pergamon, 1981
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