MA4528

MA4528 Introduction to Dynamical Systems and Chaos

Part I

Course Duration: One semester
Credit Units: 3
Level: B4
Medium of Instruction: English
Prerequisites: MA3511
Precursors: Nil
Equivalent Courses: Nil
Exclusive Courses: Nil

Part II

Course Aims
This course introduces fundamental concepts of dynamical systems and chaos with the help of computer experimentations. It helps students understand how the nonlinear property may give rise to rich complex phenomena.

Course Intended Learning Outcomes (CILOs)
Upon successful completion of this course, students should be able to:

No.	CILOs	Weighting (if applicable)
1.	explain clearly basic ideas of dynamical systems and nature of chaotic behavior.	2
2.	analyze parametric families of mappings and their applications in modeling dynamical systems.	3
3.	describe properties of solutions of (non-linear) differential equations and their applications in modeling continuous-time dynamical systems.	3
4.	apply mathematical techniques of dynamical systems and chaos in modeling real-life phenomena/systems.	2
5.	the combination of CILOs 1-4	3

Teaching and Learning Activities (TLAs)
(Indicative of likely activities and tasks designed to facilitate students’ achievement of the CILOs. Final details will be provided to students in their first week of attendance in this course)

TLAs	CILO No.	Hours/week
Learning through teaching is primarily based on lectures.	1--5	39 hours in total
Learning through take-home assignments helps students understand concepts and techniques of dynamical systems and chaos, as well as their applications in sciences.	1--4	after-class
Learning through project helps students implement mathematical and computational methods of dynamical systems/chaos to model and analyze more sophisticated physical phenomena. It also helps students to communicate and collaborate effectively in the team.	4	after-class

Assessment Tasks/Activities
(Indicative of likely activities and tasks designed to assess how well the students achieve the CILOs. Final details will be provided to students in their first week of attendance in this course)

30% Coursework
70% Examination (Duration: 3 hours, at the end of the semester)

For a student to pass the course, at least 30% of the maximum mark for the examination must be obtained.

Assessment Tasks/Activities	CILO No.	Weighting (if applicable)	Remarks
Test	1--2	15-30%	Questions are designed for the first part of the course to see how well students have learned basic concepts of dynamical systems and analyzed such systems with appropriate mappings.
Hand-in assignments	1--4	0--15%	These are skills based assessment which enables students to design and implement methods of dynamical systems and chaos in a range of application problems.
Project	4	0--15%	Students are assessed on their ability in applying concepts and techniques of dynamical systems and chaos to model physical phenomena, as well as on its presentation with analysis.
Examination	5	70%	Examination questions are designed to see how far students have achieved their intended learning outcomes. Questions will primarily be skills and understanding based to assess the student’s versatility in concepts and methods of dynamical systems and chaos.
Formative take-home assignments	1--4	0%	The assignments provide students chances to demonstrate their achievements on dynamical systems and chaos learned in this course.

Grading of Student Achievement: Refer to Grading of Courses in the Academic Regulations

Part III

Keyword Syllabus
Examples of chaotic dynamical systems. Fixed points, periodic points, Poincare-Bendixson theorem. Bifurcation theory, Hopf bifurcation, period doubling cascade. Hyperbolic invariant sets, attractors. Chaos, Liapunov exponents, fractal dimensions, topological entropy.

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1--4

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5

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