EMTH415-12S2 (C) Semester Two 2012

Special Topic in Engineering Mathematics

15 points, 0.1250 EFTS
09 Jul 2012 - 11 Nov 2012


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.

Learning Outcomes

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
    • University Graduate Attributes

      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.

Streams Day Time Where Notes
Stream 01 Tuesday 4:00pm-5:00pm E6 Lecture Theatre 3 Sep - 14 Oct
Wednesday 10:00am-11:00am Erskine 031 Lecture Theatre 3 Sep - 14 Oct
Thursday 11:00am-12:00pm Erskine 445 3 Sep - 14 Oct

Course Coordinator / Lecturer

Michael Plank


Rua Murray


Assessment Due Date Percentage 
Internal Assessment - TBA 40%
Final Examination 60%

Examination and Formal Tests

Exam Wednesday 24 Oct 2012 2:30pm-4:30pm  


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.

Course links

MATH363 Homepage

Indicative Fees

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.

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