Unit name | Applied dynamical systems |
---|---|
Unit code | MATHM0010 |
Credit points | 10 |
Level of study | M/7 |
Teaching block(s) |
Teaching Block 2C (weeks 13 - 18) |
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 |
Unit aims
The aims of this unit are:
General Description of the Unit
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.
NOTE: This unit is also part of the Oxford-led Taught Course Centre (TCC), and is taken by first- and second-year PhD students in Bristol and its TCC partner departments. The unit has been designed primarily with a postgraduate audience in mind. Undergraduate students should not normally take more than one TCC unit per semester.
Relation to Other Units
This is intended as a standalone course for students with the relevant prerequisites. A complementary (pure mathematics) perspective is given in Dynamical Systems and Ergodic Theory, and more detail on bifurcation analysis may be found in the Engineering unit Nonlinear Dynamics and Chaos. Connections may also be made with Statistical Mechanics and with applied probability units.
Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/
Learning Objectives
A student completing this unit successfully will be able to:
Transferable Skills
Mathematical modelling, computational, written and oral communication skills.
The unit will be delivered through lectures as well as written and computational homework problems.
60% Examination and 40% Coursework.
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.