Dynamical Systems

ANNOUNCEMENT

Walk in consultation 5 Nov from 13:30-15:00

Come if you have questions

2024 Slides on 1 D Maps

IPython notebook Example

Interesting Interview with Travis Oliphant who wrote NumPy, SciPy, Anaconda

Course Code MATA3784/MATZ6824 UFS 16 Credits

Overview

This course explores various aspects of nonlinear dynamical systems and chaos. It expands and applies the knowledge obtained in a first course of solving ordinary differential equations to more complex nonlinear problems. Concrete examples and geometric intuition are important aspects of the course. Concepts such as phase plane analysis, limit cycles bifurcations and stability are introduced for both linear and nonlinear systems. Regular and Singular perturbation methods as well as techniques for describing fully chaotic systems are introduced. Classic topics such as the Mathieu's equation, Lorenz equations, iterated maps, period doubling, renormalisation are touched upon. See provisional course planner below for greater detail.

Prerequisites

A first course in ordinary differential equations (MATA 2644) on the level of A first Course in Differential Equations - Dennis G Zill

Lecturer

Jeandrew Brink, Contact: BrinkJ2@ufs.ac.za , WWG 109

Course Material

Nonlinear Dynamics and Chaos: with applications to physics, biology, chemistry and engineering. Stephen Strogatz (Main text Topics from Parts 2 and 3)

Notes, articles assignments posted on this webpage.

Other good references

Non-linear ordinary differential equations. DW Jordan and P Smith 2nd Ed Claredon

Classical Mechanics. Herbert Goldstein. 2nd Ed

Regular and Chaotic Dynamics. Lichtenberg & Lieberman 2nd Ed

Lectures and Tutorials

Lecture 1: Tuesday 9:10 to 10:00 WWG 113

Lecture 2: Tuesday 10:10 to 11:00 WWG 114

Tutorial Wednesday 15:10-17:00 WWG 226

Lecture 3 Thursday 11:10 to 12:00 WWG 226 (Tutorial due)

**Lectures, discussion sessions may be held in the tutorial session.

Consultation hours

Tue 11:00-12:00

Thurs 12:00-13:00

Evaluation

There are 2 semester tests:

Test 1: Tuesday 20 August 9:00-11:00 WWG114

Test 2: Tuesday 1 October 9:00-11:00 WWG114

Each test counts 35 % of the semester mark. The tutorial test, assignments and essay presentation make up the remainder of the semester mark, namely 30 %.

A semester mark of 45% or more must be attained to gain admission to the exam. An exam mark of at least 40 % must be attained to pass the course.

In the final mark, the semester mark and exam result are weighted evenly. A final mark of at least 50 % must be attained to pass the course.

Tutorials

Semester Test 2 Memo

Tut 5 Practice Problems

Tut 5 Some Ans

Tutorial 4 Tutorial 4 Answers

Conputer Test Instructions for Tuesday 17 Sept

Tutorial 3 Due Wed 14 August Tutorial 3 Some Ans

Tutorial 2 Some ans

Class test 2 Memo

Tutorial 2 Link Class Test 30 July 10-11

Tutorial 1 Link Class Test 23 July 10-11am

Essay Topics Link, READ first, then go to Essay SIGN UP Form

Presentation Program Starting at 15:00 WWG 226

Presentation Topics Link, READ first, then go to Presentation SIGN UP Form

The presentations will take place on Wednesday Afternoon 16 October 15.00-17.00 WWG 226.

Grading Policy

No tutorials will be accepted after the due date. Tutorials that are scanned and emailed must be combined in 1 document smaller than 5Mb.

Some tutorials will be evaluated by means of a class tests that will be held during the tutorial session on Wednesday in this case the tutorials serve as preparation for the type of question to be asked during the class test. Other tutorials must be submitted in full to be graded, the nature of evaluation will be indicated on the tutorial.

The essay and presentation thereof will also help form part of the semester mark.

In the unfortunate circumstance of missing a semester test, the lecturer must be notified within 24 h. In the case of illness, a doctors certificate must be provided. A make up / special test, may be oral and/or written and will cover all the semesters work.

Note there is a NEW requirement for this semester, the faculty has decided that a student will need a minimum of 80% class/tutorial attendance. ‘’Students who do not attend at least 80% of the tutorials, contact sessions and online assessments will get an incomplete for the module.’’

Great emphasis is placed on original, creative work. A well argued, understood, possibly numerically ''wrong'' answer is of much better value than one copied from a solution manual. Collaboration on homework sets is allowed provided collaborators are given credit, and the person handing in the answer can defend the reasoning. If other sources are used, such as, books, articles etc they must be referenced. Should plagiarism be suspected, a student will be asked to solve a similar problem on the blackboard during a tutorial session, in front of the class, to obtain the marks for the tutorial.