Department of Mathematics, University of Surrey, Guildford UK
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 Timetable for Lectures

Day	Time	Room	Notes
Monday	3pm	TB06
Monday	4pm	TB06
Tuesday	9am	LTB
Wednesday	11am	AP1
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Complete Calendar for Spring 2012

 News and Announcements

* The mock exam was held on Monday 14 May. An electronic copy of the mock examination paper is available below for downloading.

* The last lecture of the semester will be Wednesday 16 May. We will discuss the solutions of the mock examination.

* Unassessed coursework #2 is now available for downloading (see below for link). A sketch of the solutions for UCW #2 is now also available for downloading (see below).

 Lecturer

The Lecturer is Prof T.J. Bridges. His office is Room 38 AA 04, and email address is T.Bridges@surrey.ac.uk .

 Introduction and overview

This module introduces the study of curves and surfaces in Euclidean space. The geometry of curves involves the concept of torsion (twisting out of a plane) and curvature (twisting away from a line), and the geometry of surfaces involves the mean and gaussian curvatures (the bending away from a plane). The topics covered include arc length, Frenet frames, calculus on curves and surfaces, tangent vectors of curves and surfaces, geodesics (as shortest paths) on surfaces, normal vector of a surface, and integration along surfaces. Examples of surfaces are spheres, tori, ruled surfaces, surfaces of revolution, and minimal surfaces. Examples from mechanics, computer graphics and other areas are used for illustration. The module consists of five parts

• Planar curves: representation, arc-length, parametrisation, curvature
• Space curves: representation, arc-length, parametrisation, curvature, torsion
• 2D surfaces in 3D: representation, tangent space, normal space, metrics, calculus
• Paths in surfaces: geodesics, length and speed, parallel transport
• Curvature of surfaces: mean curvature, gaussian curvature, implications of curvature

• A summary of topics that should be revised in preparation for the start of lectures is here

 Coursework Information

The coursework component of the module has two components: unassessed problem sheets that are worked out at home, but there is no mark associated with them. They provide preparation for the class tests and the examination. The second component is the class tests. There will be two class tests, the first counts 12% and the second 13% towards the overall mark. After they are handed out, electronic copies of the problem sheets will be available here for downloading.

• Unassessed coursework # 1: question sheet in downloadable format   (available for downloading)
• Sketch of solutions for Unassessed CW #1   (available for downloading)
• Unassessed coursework # 2: question sheet in downloadable format   (available for downloading)
• Sketch of solutions for Unassessed CW #2   (available for downloading)

 Class Tests

There will be two Class Tests in 2012 and the dates and locations will be posted below.

Class test 1 will take place on Wednesday 29 February and it will cover the following topics:

• plane curves (representation, regularity, speed, arclength, curvature)
• space curves (representation, regularity, speed, arclength, curvature, torsion, vector cross product, Frenet-Serret frame)

Class test 2 will take place on Wednesday 28 March and it will cover the following topics:

• representation of surfaces: coordinate charts, tangent space, normal
• first fundamental form: curves in surfaces, area on a surface
• curvature: Weingarten matrix, principal curvature, Gaussian curvature, mean curvature

 Assessment timetable

Assessment	% of Mark	Date	Notes
Problem sheet 1	0 %	No specific due date	Available from Monday 20 February
Class Test 1	12 %	Wednesday 29 February	Room: AP1
Problem sheet 2	0 %	No specific due date	Available from Monday 19 March
Class Test 2	13 %	Wednesday 28 March	Room: AP1
Examination	75 %	Friday 8 June	TBA

 Reference Textbook

There is no particular textbook. The lecture notes provide the basic information required for the course. A reference text which covers some of the same material as the lecture course is

Andrew Pressley [2001]  Elementary Differential Geometry,
Springer-Verlag: London, ISBN 1852331526

There are several copies in the University Library, and copies can be purchased through the University of Surrey Bookshop .
New and used copies can also be ordered over the web from http://www.amazon.co.uk

 Past examination papers

The module MAT2047 is new and so there are no past examination papers.
A mock examination was held on Monday 14 May and an electronic copy is available for downloading
here. (available for downloading)

 Links

• National Curve Bank: Index of Classic Plane Curves and Surfaces
• Visualizing the fourth dimension
• Geodesics on a torus
• The three sphere, quaternions and rotation matrices
• Holonomy
• Link to the University Module Catalogue entry for MAT2047
• Department Homepage
• University of Surrey Website

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Disclaimer

Every effort has been made to ensure the accuracy of the information contained in the University's web pages and in the associated School/Department pages. The University reserves the right to make changes to the information given. Applicants will receive additional, current information during the admissions process and on joining the University.

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