- Four Weeks
- Tanya Schmah (Macquarie University)
- Tuesday 12-13, 14-15 in Carslaw Room 609. (These are times when I promise
to be there and available. Please feel free to make an appointment, or just drop by, at other times.
- 80% final exam (Friday 9 Feb 9–11 in Carslaw Room 275), 20% assignments.
- A good grounding in multivariable calculus, linear algebra and introductory real
analysis, as well as some familiarity with ODEs and groups. Some experience of classical mechanics
is desirable but not necessary.
- There is an Assignment (PDF) part of which you are expected to hand in by Wednesday in
the first week (not part of the assessment). See http://www.maths.mq.edu.au/~schmah/ice07/
for more resources.
- This is an introduction to Riemannian and symplectic geometry on manifolds,
with some applications to mechanics. We begin with the geometry of parametrised surfaces,
including: Gaussian curvature; geodesics; isometries and area-preserving maps; and gradient and
skew-gradient vector fields. The second part of the course is about manifolds, including: vector
fields, tensors and forms; Lie derivatives; Frobenius’ theorem; orientation; and Lie groups. In the
latter third of the course, we formally introduce Riemannian geometry, symplectic geometry and
Hamiltonian mechanics. Time permitting, the course will conclude with an introduction to Lie
group symmetries in mechanics.