Module description
Syllabus:
Definition of a curve, arc length, curvature and torsion of a curve, Frenet-Serret equations.
Definition of a surface patch, first and second fundamental forms, isometries, conformal maps, area, Gaussian curvature, mean curvature, principal curvatures, Gauss map, geodesics, Theorema Egregium.
Prerequisites:
4CCM111a Calculus I, 4CCM112a Calculus II, 4CCM113a Linear Algebra and Geometry I or equivalent. You cannot take this module if you have already taken 5CCM223A Geometry of Surfaces
Assessment details
Written examination.
Educational aims & objectives
This module will apply the methods of calculus to the geometry of curves and surfaces in three-dimensional space. The most important idea is that of the curvature of a curve or a surface. The module should prepare you for more advanced modules in geometry, as well as courses in mathematical physics such as relativity.
Teaching pattern
Three hours of lectures and one hour of tutorial per week throughout the term
Suggested reading list
Indicative reading list - link to Leganto system where you can search with module code for lists