Module Catalogues

Geometry of Curves and Surfaces

Module Title Geometry of Curves and Surfaces
Module Level Level 3
Module Credits 5.00

Aims and Fit of Module

• To introduce the ideas and methods of the classical differential geometry of curves and surfaces in three dimensional Euclidean space.
• To translate intuitive geometrical ideas into mathematical concepts that allow for quantitative study.
• To illustrate geometrical concepts through examples.
This module builds on concepts introduced in vector analysis, and has a wide range of applications in science and technology. It provides a foundation for further study of topics such as Riemannian geometry, continuum mechanics and general relativity.

Learning outcomes

A Apply techniques from calculus and linear algebra with confidence to the study of geometrical objects
B Define and interpret the meaning of core concepts in the differential geometry of curves and surfaces in 3-dimensional space
C Calculate various quantities (e.g. length, curvature, torsion; fundamental forms, area) for given examples and interpret their geometrical significance
D Discriminate between intrinsic and extrinsic geometrical properties

Method of teaching and learning

This module will be delivered through a combination of formal lectures and tutorials.