Department of Mathematical Sciences, Unit Catalogue 2011/12 |
|
 Credits:
| 6 |
| Level:
| Honours (FHEQ level 6) |
| Period: |
Semester 2 |
| Assessment:
| CW 25%, EX 75% |
| Supplementary Assessment: | MA30060 Mandatory Extra Work (where allowed by programme regulations) |
| Requisites:
| Before taking this unit you must take MA20216 and take MA20218 and take MA20219 and take MA20220 and take MA20221 and take MA20222 |
| Description:
| Aims & Learning Objectives: Aims: The course is intended to be an elementary and accessible introduction to dynamical systems with examples of applications. Main emphasis will be on discrete-time systems which permits the concepts and results to be presented in a rigorous manner, within the framework of the second year core material. Discrete-time systems will be followed by an introductory treatment of continuous-time systems and differential equations. Numerical approximation of differential equations will link with the earlier material on discrete-time systems. Objectives: An appreciation of the behaviour, and its potential complexity, of general dynamical systems through a study of discrete-time systems (which require relatively modest analytical prerequisites) and computer experimentation. Content: Topics will be chosen from the following: Discrete-time systems. Maps from 3n to 3n. Fixed points. Periodic orbits. α and ω limit sets. Local bifurcations and stability. The logistic map and chaos. Global properties. Continuous-time systems. Periodic orbits and Poincaré maps. Numerical approximation of differential equations. Newton iteration as a dynamical system. |
| Programme availability: |
MA30060 is Optional on the following programmes:Department of Mathematical Sciences
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