Elementary Curves and Surfaces

Course description: The course is designed as an informal introduction to the geometry of curves and surfaces in space. This involves the concept of torsion (twisting out of a plane) and curvature (away from a line) of curves, and the curvature (away from a plane) of surfaces. A feature of the course is the use of the computer algebra package Mathematica (for which Manchester University has a site licence and student versions are available for personal use) to do all the calculus and graphics in computer lab sessions. All materials are available on line. Lecture Notes (PDF format).

Some animations of curves, surfaces and knots

Recommended text: A. Gray. Modern Differential Geometry of Curves and Surfaces. Boca Raton: CRC Press, Second Edition, 1998.
Mathematica Packages: Alfred Gray's Mathematica packages for curves and surfaces are free and available locally, together with others that we use, see Beginning Mathematica .
Introductory Mathematica Notebook: ==>Download and open in Mathematica

Breakdown of Lectures: Lecture Notes
5 Elementary theory of curves, their curvature and torsion
7 Elementary theory of surfaces and their curvature
12 Computer laboratory sessions investigating properties of curves and surfaces.
Coursework Assignments: ==>Download and open in Mathematica
Assignment 1 Complete and submit by end of Week 4
Assignment 2 Complete and submit by end of Week 8
Assignment 3 Complete and submit by end of Week 11

Other On-Line Mathematical Materials:


C.T.J. Dodson

Sun Jul 14 19:38:00 EDT 1996