
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: 

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 continuoustime 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 saddlenode, transcritical and Hopf bifurcation), Global bifurcations (homoclinic orbits, homoclinic bifurcations). 
Programme availability: 
MA40045 is Optional on the following programmes:Department of Computer Science
