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Unit information: Nonlinear Dynamics and Chaos in 2015/16

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Unit name Nonlinear Dynamics and Chaos
Unit code EMAT33100
Credit points 10
Level of study H/6
Teaching block(s) Teaching Block 1 (weeks 1 - 12)
Unit director Dr. Barton
Open unit status Not open
Pre-requisites

EMAT20200 Engineering Mathematics 2

Co-requisites

None

School/department Department of Engineering Mathematics
Faculty Faculty of Engineering

Description

Description: Based on a format of lively lectures combined with experiments and computer demonstrations, this unit introduces students of all disciplines to chaos theory and the profound effect that this field has had on a wide range of application areas. The course focuses on geometric techniques for analysing a system, thereby avoiding cumbersome algebraic manipulations. Of particular interest are qualitative changes of the dynamics as parameters are changed, which allows you to describe ways that a system can become chaotic.

Aims: This unit is intended to alert students to the complicated behaviour that can occur in simple systems and to equip them with the straightforward mathematical tools to analyse simple nonlinear systems. Additionally, the students will be introduced to a range of numerical methods that will allow them to investigate more complicated systems arising from real-world problems.

Intended learning outcomes

  1. Enhancement and development of students' understanding of and ability to use the language and methods of mathematics in the description, analysis and design of nonlinear systems
  2. The ability to use appropriate numerical methods to investigate the dynamics of non-trivial nonlinear systems.

Teaching details

Lectures

Assessment Details

Two-hour written examination: 80% (learning outcome 1)

Coursework: 20% (learning outcome 2)

Reading and References

  • Steven H. Strogatz, Nonlinear Dynamics and Chaos, with Applications in Physics, Biology, Chemistry, and Engineering, Addison-Wesley, 1994
  • J.M.T. Thompson & H.B. Stewart, Nonlinear Dynamics and Chaos, Wiley, 2002
  • John Guckenheimer & Philip J. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, New York, 1986
  • Yuri A. Kuznetsov, Elements of Applied Bifurcation Theory, Springer-Verlag, New York, 1995, 1998
  • Robert L. Devaney, An Introduction to Chaotic Dynamical Systems, Perseus Publishing Co., 1989
  • H.-O. Peitgen, H. J├╝rgens & D. Saupe, Chaos and Fractals, New Frontiers of Science, Springer-Verlag, New York, 1992

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