MAT3072

Geometry and analysis

(SCI)

Coordinator: Dr Tom Hall

4 points + Two 1-hour lectures and one 1-hour support class per week + Second semester + Clayton + Prerequisites: MAT2020, MAT2030 and MAT2051 + Prohibitions: MAP3102

Synopsis: Brief review of several variables, surfaces in Euclidean space given as level sets of functions, tangent planes, normal vectors and vector fields on surfaces, geodesics (curves of shortest length), parallel transport, curvature, surfaces given by coordinate systems (parametrised surfaces), local equivalence between parametrized surfaces and level sets (implicit function theorem), surface integrals, basics on differential forms and tensors, Stokes0 theorem; further topics: minimal surfaces, Gauss-Bonnet theorem.

Assessment: Examination (2 hours): 70% + Assignments: 30%