
Academic Year:  2015/6 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 
Semester 2 
Assessment Summary:  EX 100% 
Assessment Detail: 

Supplementary Assessment: 
MA40048 Mandatory extra work (where allowed by programme regulations) 
Requisites:  Before taking this module you must take MA20216 AND take MA20217 AND take MA20218 AND take MA20219 AND take MA20220 AND take MA30041 . Students may also find it useful to take MA40062 before taking this unit. 
Description:  Aims: To give a unified presention of systems of ordinary differential equations that have a Hamiltonian or Lagrangian structure. Geometrical and analytical insights will be used to prove qualitative properties of solutions. These ideas have generated many developments in modern pure mathematics, such as symplectic geometry and ergodic theory, besides being applicable to the equations of classical mechanics, and motivating much of modern physics. Learning Outcomes: Students should be able to state and prove general theorems for Lagrangian and Hamiltonian systems. Based on these theoretical results and key motivating examples they should be able to identify general qualitative properties of solutions of these systems. Skills: Numeracy T/F A Problem Solving T/F A Written and Spoken Communication F (solutions to exercise sheets, problem classes) Content: Lagrangian and Hamiltonian systems, phase space, phase flow, variational principles and EulerLagrange equations, Hamilton's Principle of least action, Legendre transform, Liouville's Theorem, Poincare recurrence theorem, Noether's Theorem. Topics from: the direct method of the Calculus of Variations, constrained variational problems, HamiltonJacobi equation, canonical transformations. 
Programme availability: 
MA40048 is Optional on the following programmes:Department of Computer Science
