MAT3037

Mathematical modelling B

Dr Alistair Carr

4 points - One 2-hour lecture and one 1-hour tutorial per week - Second semester - Gippsland/Distance (odd-numbered years only) - Prerequisites: MAT2096, MAT2030 and GCO1811 or GCO1832 (MAT2077 with MAT1060 are desirable) - Prohibitions: GAS3622

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 aided by linearisation, asymptotic stability, bifurcation, limit cycles, strange attractors, sensitive dependence on initial conditions, and chaotic solutions; to be able to apply these ideas and associated analytical methods to qualitative and quantitative investigation of 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 MAT2096. We introduce several methods 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, bifurcation, and chaotic behaviour.

Assessment Three assessment assignments: 70% - One 2-hour examination: 30% - Students must pass both the assignment work and the examination in order to receive a passing grade.

Prescribed texts

Devaney R L A first course in chaotic dynamical systems: Theory and experiment Addison-Wesley, 1992

Recommended texts

Beltrami E Mathematics for dynamic modeling Academic Press, 1987
Kapur J N Mathematical modelling Wiley, 1988
Saaty T and Alexander J Thinking with models Pergamon, 1981

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