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Academic Year: | 2015/6 |
Owning Department/School: | Department of Mathematical Sciences |
Credits: | 6 |
Level: | Masters UG & PG (FHEQ level 7) |
Period: |
Semester 1 |
Assessment Summary: | EX 100% |
Assessment Detail: |
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Supplementary Assessment: |
MA40045 Mandatory extra work (where allowed by programme regulations) |
Requisites: | Before taking this module you must take MA20216 AND take MA20218 AND take MA20219 AND take MA20220 AND take MA20221 AND take MA30041 . Students may also find it useful to take MA40062 before taking this unit. |
Description: | Aims: To provide an accessible introduction to the qualitative and geometric theory of dynamical systems to a level that will make accessible an area of mathematics that is highly active and reaches into many areas of applied mathematics. Learning Outcomes: Students should be conversant with concepts, results and techniques fundamental to the study of the qualitative behaviour of continuous-time dynamical systems. Students should be able to investigate stability of equilibria and periodic orbits and should have a basic understanding and appreciation of invariant manifolds and bifurcations. Skills: Numeracy T/F A Problem Solving T/F A Written and Spoken Communication F (in tutorials) Content: Linearisation and Hyperbolicity (stability, conjugacies, and the stable manifold theorem), Periodic solutions and the dynamics in the plane (PoincarĂ© index and the Poincaré Bendixon Theorem), Bifurcations from equilibria (Centre manifold theorem, the saddle-node, transcritical and Hopf bifurcation), Global bifurcations (homoclinic orbits, homoclinic bifurcations). |
Programme availability: |
MA40045 is Optional on the following programmes:Department of Computer Science
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