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Special Topic in Engineering Mathematics
Dynamical systems is the study of global, long-term behaviour of mathematical systems whose state evolves with time. Most of the systems studied arise from differential equations models of an applied problem from Physics, Biology, Economics, Chemistry, Engineering, etc. The aim of this course is to understand asymptotic behaviour using a combination of geometric reasoning, intelligent approximations, computer assistance and mathematical insight. This will be accomplished without grinding out the solutions of special classes of differential equations.Topics covered: Overview of dynamics; flows on the line; one and two parameter bifurcations; 2d linear systems; phase plane for nonlinear 2d systems; limit cycles; Hopf bifurcations; applications; introduction to chaos in 3d flows.
to develop insight into the qualitative behaviour of the solutions to differential equations; in particular, the effects of nonlinearity to obtain a greater understanding of the use of differential equations in modelling physical systems; including the role of parameters, and the interplay between solutions to the model and experiments to apply relevant computational and geometric techniques to analyse systems of differential equations; and to communicate the mathematical results clearly and coherently
This course will provide students with an opportunity to develop the Graduate Attributes specified below:
Critically competent in a core academic discipline of their award
Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.
Subject to approval of Head of Department.
The required text is:Steven H Strogatz, Nonlinear dynamics and chaos with applications to Physics, Biology, Chemistry and Engineering, ISBN 0-7382-0453-6, Westview Press (Perseus Books Publishing), Cambridge, MA, 2000.Other recommended reading:Jim Meiss Differential dynamical systems, SIAM, 2007.This is an excellent text which includes proofs of many of the important theorems; it also includes many other interesting things.
Domestic fee $777.00
International fee $4,375.00
* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.
For further information see
Mathematics and Statistics.