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MA40045: Dynamical systems

Follow this link for further information on academic years Academic Year: 2012/3
Follow this link for further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Follow this link for further information on credits Credits: 6
Follow this link for further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Follow this link for further information on period slots Period: Semester 1
Follow this link for further information on unit assessment Assessment: EX 100%
Follow this link for further information on supplementary assessment Supplementary Assessment: Like-for-like reassessment (where allowed by programme regulations)
Follow this link for further information on unit rules Requisites: Before taking this unit 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.
Follow this link for further information on unit content 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
(Poincaré 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).
Follow this link for further information on programme availabilityProgramme availability:

MA40045 is Optional on the following programmes:

Department of Computer Science
  • USCM-AFM14 : MComp (hons) Computer Science and Mathematics (Full-time) - Year 4
  • USCM-AKM14 : MComp (hons) Computer Science and Mathematics with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 5
  • USCM-AAM14 : MComp (hons) Computer Science and Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 5
Department of Mathematical Sciences
  • USMA-AFM14 : MMath Mathematics (Full-time) - Year 4
  • USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • TSMA-AFM09 : MSc Mathematical Sciences (Full-time) - Year 1
  • TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 1
  • TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 2
  • TSMA-AFM08 : MSc Modern Applications of Mathematics (Full-time) - Year 1
  • TSMA-AFL02 : PG Dip Modern Applications of Mathematics (Full-time) - Year 1

Notes:
* This unit catalogue is applicable for the 2012/13 academic year only. Students continuing their studies into 2013/14 and beyond should not assume that this unit will be available in future years in the format displayed here for 2012/13.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.