Module Title
Geometry of Curves and Surfaces

Module Level
Level 3

Module Credits
5.00

Academic Year
2024/25

Semester
SEM1

• 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.

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

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