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 University | Catalogues for 2006/07

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Department of Mathematical Sciences, Unit Catalogue 2006/07

MA40048 Analytical & geometric theory of differential equations

Credits: 6
Level: Masters
Semester: 1
Assessment: EX100
Before taking this unit you must take MA20007 and take MA20008 and take MA20009 and take MA20010 and take MA20011 and take MA20012 and take MA20013 and take MA40062

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.
Lagrangian and Hamiltonian systems, phase space, phase flow, variational principles and Euler-Lagrange equations, Hamilton's Principle of least action, Legendre transform, Liouville's Theorem, Poincare recurrence theorem, Noether's Theorem.


University | Catalogues for 2006/07