Faculty of Science

Objectives

To introduce differential geometry.

Contents

Normed vector spaces and differentiation: Norms, equivalence of norms, maps and continuity of maps between normed spaces; Fréchét differentiability and properties; Differential Geometry: n-surfaces, integral curves, level sets, surfaces of revolution, generalisation of the Lagrange Multiplier theorem; Geodesics and parallel transport; The Wergarten map and curvature.

Prerequisite: