Department of Mathematical Sciences, Unit Catalogue 2011/12 

Credits:  6 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 
Semester 1 
Assessment:  EX 100% 
Supplementary Assessment:  Likeforlike reassessment (where allowed by programme regulations) 
Requisites:  Before taking this unit you must take MA20216 and take MA20218 and take MA20219 and take MA20220 and take MA20221 and take MA30041 and take MA40062 
Description:  Aims & Learning Objectives: Aims: To give a unified presention of systems of ordinary differential equations that have a Hamiltonian or Lagrangian structure. Geomtrical and analytical insights will be used to prove qualitative properties of solutions. These ideas have generated many developments in modern pure mathematics, such as sympletic geometry and ergodic theory, besides being applicable to the equations of classical mechanics, and motivating much of modern physics. Objectives: Students will be able to state and prove general theorems for Lagrangian and Hamiltonian systems. Based on these theoretical results and key motivating examples they will identify general qualitative properties of solutions of these systems. 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. 
Programme availability: 
MA40048 is Optional on the following programmes:Department of Mathematical Sciences
