MATH363-15S2 (C) Semester Two 2015

Dynamical Systems

15 points

Details:
Start Date: Monday, 13 July 2015
End Date: Sunday, 15 November 2015
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 26 July 2015
  • Without academic penalty (including no fee refund): Sunday, 11 October 2015

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

Prerequisites

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

Course Coordinator / Lecturer

Rua Murray

Lecturer

Mark Hickman

Assessment

Assessment Due Date Percentage 
Assignments 40%
Final Examination 60%


In order to pass this course you must both pass the course as a whole (≥50%) and obtain at least 40% in the final examination.

Indicative Fees

Domestic fee $699.00

International fee $3,450.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All MATH363 Occurrences

  • MATH363-15S2 (C) Semester Two 2015
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