Dynamical Systems and Chaos

Subject MAST20019 (2010)

Note: This is an archived Handbook entry from 2010.

Credit Points: 12.50
Level: 2 (Undergraduate)
Dates & Locations:

This subject has the following teaching availabilities in 2010:

Semester 2, Parkville - Taught on campus.
Pre-teaching Period Start not applicable
Teaching Period not applicable
Assessment Period End not applicable
Last date to Self-Enrol not applicable
Census Date not applicable
Last date to Withdraw without fail not applicable

Lectures, practice classes and computer laboratory classes.

Timetable can be viewed here. For information about these dates, click here.
Time Commitment: Contact Hours: 3 x one hour lectures per week, 8 x one hour practice classes during the semester, 4 x one hour computer laboratory classes during the semester (Either a practice class or a computer lab will run each week.)
Total Time Commitment: Estimated total time commitment of 120 hours
Prerequisites:

One of

and one of

  • 620-156 Linear Algebra
  • 620-157 Accelerated Mathematics 1
  • 620-122 Mathematics B Advanced (prior to 2008)
  • 620-190 UMEP Maths for High Achieving Students
  • 620-194 Mathematics B Advanced (prior to 2006)
  • 620-211 Mathematics 2 Advanced (prior to 2008)
  • 620-142 Mathematics B (prior to 2009)
  • 620-192 Mathematics B (prior to 2006)
Corequisites: None
Recommended Background Knowledge: None
Non Allowed Subjects: None
Core Participation Requirements: It is University policy to take all reasonable steps to minimise the impact of disability upon academic study and reasonable steps will be made to enhance a student’s participation in the University’s programs. Students who feel their disability may impact upon their participation are encouraged to discuss this with the subject coordinator and the Disability Liaison Unit.

Coordinator

Prof John Sader

Contact

Second Year Coordinator

Email: sycoord@ms.unimelb.edu.au

Subject Overview: This subject introduces the basic concepts and tools of dynamical systems and chaos. It will encompass systems that are discrete and continuous in time, and explore the practical applications from which they may arise. The subject discusses under what conditions chaos exists and the intricate array of phenomena that arise from non-linear dynamical systems. This will include the generation of fractal patterns such as the Mandelbrot and Julia sets and a discussion of self-similar structure, which has proved useful in areas such as image compression. In short, the subject will present an exposition of basic mathematical theorems and develop their application through sample dynamical systems. This will empower the student with tools and knowledge for interpreting real world phenomena.
Objectives:

On completion of this subject, students should:

  • Appreciate the wide range of scientific areas that give rise to discrete and continuous dynamical systems
  • Understand how simple dynamical systems can produce complex behaviour
  • Be able to determine local stability of solutions in simple discrete and continuous dynamical systems
  • Learn how dynamical systems can change their qualitative behaviour as a parameter is varied
Assessment:

Two computer based assignments due mid-semester and at the end of semester (20%), and a 3-hour written examination in the examination period (80%).
Prescribed Texts: None
Breadth Options:

This subject potentially can be taken as a breadth subject component for the following courses:

You should visit learn more about breadth subjects and read the breadth requirements for your degree, and should discuss your choice with your student adviser, before deciding on your subjects.

Fees Information: Subject EFTSL, Level, Discipline & Census Date
Generic Skills:

In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:

  • problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
  • analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
  • collaborative skills: the ability to work in a team;
  • time management skills: the ability to meet regular deadlines while balancing competing commitments.
  • computer skills: the ability to use mathematical computing packages.
Notes: This subject is available for science credit to students enrolled in the BSc (both pre-2008 and new degrees), BASc or a combined BSc course.

Students undertaking this subject are required to access a computer with the software Matlab installed, currently in every open-access campus laboratory.

Students are expected to use the software Matlab but no programming knowledge is expected.
Related Course(s): Bachelor of Science

Download PDF version.