Unit name | Applied dynamical systems |
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Unit code | MATHM0010 |
Credit points | 10 |
Level of study | M/7 |
Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
Unit director | Professor. Dettmann |
Open unit status | Not open |
Pre-requisites |
MATH11005 (Linear Algebra and Geometry), MATH11006 (Analysis 1), MATH 20101 (Ordinary Differential Equations), MATH 20700 (Numerical Analysis). MATH36206 or MATHM6206 (Dynamical Systems and Ergodic Theory) is helpful but optional. Students will be expected to have attained a degree of mathematical maturity and facility at least to the standard of a beginning Level M/7 student. |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
This unit provides an introduction to dynamical systems from an applied mathematics point of view, surveying the main areas of the subject, with an emphasis on concepts and on analytical and numerical methods that form a foundation for research in applied mathematics and theoretical physics. Systems considered range from almost regular through intermittent to strongly chaotic. Relevant geometrical structures such as bifurcation diagrams, fractal attractors and repellers are discussed at the relevant points. While the unit is self-contained, it is advantageous to first complete Dynamical Systems and Ergodic Theory, available at level H/6 or M/7, which emphasises hyperbolic and ergodic dynamics from a pure mathematics perspective.
The aims of this unit are:
A student completing this unit successfully will be able to:
The unit will be delivered through lectures. The lectures will be transmitted over the internet as part of the Taught Course Centre (TCC). The TCC is a consortium of five mathematics departments, including Bath, Bristol, Imperial College, Oxford and Warwick.
Formative homework exercises will be assigned throughout the unit, both theoretical and numerical.
The final assessment mark will be based on:
where the requirements for the project and the presentation will include a brief literature survey, and analytical and numerical investigations of a dynamical system.