Undergraduate Course: Dynamical Systems (MATH11027)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 11 (Year 4 Undergraduate) |
Credits | 10 |
| Home subject area | Mathematics |
Other subject area | Specialist Mathematics & Statistics (Honours) |
| Course website |
https://info.maths.ed.ac.uk/teaching.html |
Taught in Gaelic? | No |
| Course description | Course for final year students in Honours programmes in Mathematics.
Concepts of continuous and discrete dynamical systems. Orbits, fixed points and periodic orbits. Poincare maps. Classification of fixed points for linear discrete systems. Fixed points in nonlinear systems: stable and unstable manifolds. Bifurcation theory for one and two dimensional systems: saddle-node, flip and Hopf bifurcations. Logistic map: period-doubling cascade and chaos. Chaotic attractors and fractals. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | Yes |
Course Delivery Information
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| Delivery period: 2014/15 Semester 2, Available to all students (SV1)
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Learn enabled: Yes |
Quota: None |
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Web Timetable |
Web Timetable |
| Course Start Date |
12/01/2015 |
| Breakdown of Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )
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| Additional Notes |
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| Breakdown of Assessment Methods (Further Info) |
Written Exam
95 %,
Coursework
5 %,
Practical Exam
0 %
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| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
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| Main Exam Diet S2 (April/May) | Dynamical Systems | 2:00 | |
Summary of Intended Learning Outcomes
1. Ability to identify and classify of fixed points of discrete systems.
2. Ability to construct of stable and unstable manifolds for nonlinear systems.
3. Ability to calculate an appropriate normal form for nonlinear systems and thereby deduce the stability of fixed points.
4. Ability to characterise saddle-node, flip and Hopf bifurcations.
5. Appreciation of the period-doubling cascade and the notion of chaotic systems.
6. Ability to calculate Liapunov exponents.
7. Familiarity with attractors and basins of attraction.
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Assessment Information
| See 'Breakdown of Assessment Methods' and 'Additional Notes', above. |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Not entered |
| Transferable skills |
Not entered |
| Reading list |
Not entered |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | DSy |
Contacts
| Course organiser | Dr Jacques Vanneste
Tel: (0131 6)50 6483
Email: |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: |
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