MA40045: Dynamical systems
[Page last updated: 05 August 2021]
Academic Year:  2021/2 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 

Assessment Summary:  EX 100% 
Assessment Detail: 

Supplementary Assessment: 

Requisites:  Before taking this module you must take MA20221 
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 (Poincaré 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 Mathematical Sciences

Notes:
