Dynamical Systems and Chaos

This subject has the following teaching availabilities in 2012:

Lectures, practice classes and computer laboratory classes.

Estimated total time commitment of 120 hours

One of

And one of

• 620-296 Multivariable and Vector Calculus (prior to 2010)
• 620-231 Vector Analysis (prior to 2009)
• 620-233 Vector Analysis Advanced (prior to 2009)

None

None.

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For the purposes of considering request for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Students Experiencing Academic Disadvantage Policy, academic requirements for this subject are articulated in the Subject Description, Subject Objectives, Generic Skills and Assessment Requirements of this entry.
The University is dedicated to provide support to those with special requirements. Further details on the disability support scheme can be found at the Disability Liaison Unit website: http://www.services.unimelb.edu.au/disability/

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.

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

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%).

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

• Bachelor of Arts
• Bachelor of Commerce
• Bachelor of Environments
• Bachelor of Music

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.

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.

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.

MAST20019 Dynamical Systems and Chaos will be offered for the last time in semester 2, 2012.