Mathematics of chaos and fractals
Coordinator: Professor Joe Monaghan
6 points * Three 1-hour lectures per week, one 1-hour tutorial * Second semester * Clayton * Prerequisites: At levels 3 and 4,VCE Mathematical Methods * Prohibitions: MAA2021
Objectives On the completion of this subject students will be able to appreciate and understand chaotic discrete systems using elementary mathematical concepts; study the dynamics of one dimensional discrete systems and determine conditions under which they reach a steady state, oscillate or eventually become chaotic; analyse in some detail the logistic equation and similar systems and examine the phenomena of period doubling and universality; apply the mathematics to physical and biological contexts, including population modelling; understand how dynamical systems produce fractals, in particular Mandelbrot and Julia sets.
Synopsis Theory, modelling and evolution of discrete dynamical systems. Deterministic and chaotic systems: investigations and applications to physical, biological and ecological systems. The logistic equation, fractals, Julia sets and Mandelbrot sets. Two- dimensional maps. Use of the computer algebra package DERIVE.
Assessment Examinations (2 hours): 85% * Assignments/Tests: 15% or as announced at the beginning of the teaching year
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