modules

On this module, you will have the opportunity to study mathematical topics involving differential geometry of curves and surfaces, and calculus on manifolds. You will learn about various topics in differential geometry such as curves in space and curvature, manifolds and coordinate charts, classification of surfaces, the fundamental equations of surfaces, Gaussian and mean curvatures, and the Gauss-Bonnet theorem. You become familiar with differential forms, integration and differentiation of differential forms, and the generalised Stokes’ theorem. Furthermore, you will learn about formalism of tensors. This includes covariant and contravariant tensors, tensor fields, elementary operations with tensors, the Lie derivative, the affine connection and covariant differentiation, geodesic coordinates, the metric, and the curvature tensor, as well as the Euler–Lagrange equations and variational methods for geodesics.

 

Pre-requisite modules: MTH2004 Vector Calculus and Applications, MTH2003 Differential Equations, or equivalent