MATH363-20S2 (C) Semester Two 2020

Dynamical Systems

15 points

Details:
Start Date: Monday, 13 July 2020
End Date: Sunday, 8 November 2020
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Friday, 24 July 2020
  • Without academic penalty (including no fee refund): Friday, 25 September 2020

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
EMTH210 and a further 15 points from (EMTH211, EMTH271, MATH202, MATH203, MATH240, MATH270).

Restrictions

Timetable 2020

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Monday 11:00 - 12:00 E14 Lecture Theatre
13 Jul - 23 Aug
7 Sep - 18 Oct
Lecture B
Activity Day Time Location Weeks
01 Thursday 12:00 - 13:00 E16 Lecture Theatre
13 Jul - 23 Aug
7 Sep - 18 Oct
Computer Lab A
Activity Day Time Location Weeks
01 Wednesday 13:00 - 14:00 Jack Erskine 035 Lab 2 13 Jul - 23 Aug
7 Sep - 18 Oct
02 Wednesday 14:00 - 15:00 Jack Erskine 035 Lab 2 13 Jul - 23 Aug
7 Sep - 18 Oct

Course Coordinator / Lecturer

Alex James

Lecturer

Michael Plank

Indicative Fees

Domestic fee $780.00

International fee $4,250.00

* 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.

All MATH363 Occurrences

  • MATH363-20S2 (C) Semester Two 2020