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.
Assessment details
Written examination or alternative assessment.
Exercises or quizzes will be set each week to be handed in the following week. These problems will be discussed in the tutorials and solutions will be available.
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