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MX4555: NONLINEAR DYNAMICS & CHAOS THEORY II (2017-2018)

Last modified: 25 May 2018 11:16


Course Overview

This second part of the course covers more advanced mathematical concepts required for the description of dynamical systems. It continues the study of nonlinear systems, for which typically no analytical solutions can be found; these systems are pivotal for the description of natural systems.

Emphasis will be on the study of higher dimensional and chaotic systems. This second part of the course introduces stability criteria for more complex systems and outlines several key results that govern the behaviour of nonlinear dynamical system, such as requirements for chaotic behaviour and recurrence properties.


Course Details

Study Type Undergraduate Level 4
Session Second Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus None. Sustained Study No
Co-ordinators
  • Professor Marco Thiel

Qualification Prerequisites

  • Programme Level 4

What courses & programmes must have been taken before this course?

  • MA1006 Algebra (Passed)
  • Either MX4084 Nonlinear Dynamics & Chaos Theory (Studied) or MX4085 Nonlinear Dynamics & Chaos Theory I (Studied)
  • MA1508 Calculus II (Passed)
  • Any Undergraduate Programme (Studied)
  • MA1005 Calculus 1 (Passed)

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

Course Description

This course covers advanced mathematical concepts required for the description of dynamical systems, ie., systems that change in time. It discusses nonlinear systems, for which typically no analytical solutions can be found; these systems are pivotal for the description of natural systems in physics, engineering, biology etc. Some emphasis will be on the study of chaotic systems and strange, ie., fractal attractors.

Next to the theory of relativity and quantum mechanics, chaos and dynamical systems theory has been considered as one of three major advances in the natural sciences. This course covers the mathematics behind this paradigm changing theory.

Further Information & Notes

Course Aims

This course covers the fundamental mathematical concepts required for the description of dynamical systems, i.e., systems that change in time. It discusses ordinary differential equations and nonlinear systems, for which typically no analytical solutions can be found; these systems are pivotal for the description of natural systems in physics, engineering, biology etc. Some emphasis will be on the study of chaotic systems and strange, i.e., fractal attractors.
 
Next to the theory of relativity and quantum mechanics, chaos and dynamical systems theory is considered as one of three major advances in the natural sciences. This course covers the mathematics behind this paradigm changing theory. See the end of this document for a more detailed syllabus.

 

Learning Objectives
By the end of the course the student should:
- be familiar with basic mathematical concept required for the description of linear as well as nonlinear dynamical systems.
- be familiar with various concepts and procedures to solve ordinary differential equations.
- be familiar with the mathematical theory underlying ordinary differential equations and their solutions.
- be familiar with the various approaches to characterise chaotic systems, know about their properties and be familiar with the underlying theory.

Degree Programmes for which this Course is Prescribed

  • BSc Applied Mathematics
  • MA Applied Mathematics

Contact Teaching Time

33 hours

This is the total time spent in lectures, tutorials and other class teaching.

Teaching Breakdown


Assessment

1st Attempt: 1 two-hour written examination (70%); 1 one-hour midterm exam  (30%).

Resit: Written Exam (100%).

Only the marks obtained at the first attempt can count towards Honours classification. 

Formative Assessment

By weekly tutorials and dialogue with lecturer. 

Feedback

Within two weeks of midterm exam.

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