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MATH363-12S2 (C) Semester Two 2012
Dynamical Systems

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

An introduction to nonlinear systems, the use of linearisation techniques and bifurcation theory.

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

Pre-requisites

MATH201 or MATH264 or (MATH261 and MATH262) or EMTH202 or EMTH204 or EMTH210 and a further 15 points from (EMTH211, EMTH271, MATH202, MATH203, MATH240, MATH270).

Restrictions

Lectures
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

Lecturer

Rua Murray

Assessment

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

Examination and Formal Tests

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

Textbooks

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

Fees

Domestic fee $622.00
International fee $3,200.00


For further information see Mathematics and Statistics.

All MATH363 Occurrences

  • MATH363-12S2 (C) Semester Two 2012
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