# Geometry Of Surfaces

King's College London

## Course Description

• ### Course Name

Geometry Of Surfaces

• ### Host University

King's College London

• ### Location

London, England

• ### Area of Study

Geometry, Mathematics

• ### Language Level

Taught In English

• ### Course Level Recommendations

Upper

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• UK Credits

15
• Recommended U.S. Semester Credits
4
• Recommended U.S. Quarter Units
6
• ### Overview

Geometry Of Surfaces
Module code: 5CCM223A
Semester: Semester 2 (spring)
Module description:
Aims and 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.
Pre-requisites 4CCM111A Calculus I, 4CCM112A Calculus II, 4CCM113A Linear Methods.
Syllabus:
Definition of a curve, arc length, curvature and torsion of a curve, Frenet-Serret equations. Definition of a surface patch, first fundamental form, isometries, conformal maps, area of a surface. Second fundamental form of a surface, gaussian, mean and principal curvatures. Gauss map. Theorema Egregium. Geodesics. Gauss-Bonnet theorem.
Books:
Credit level: 5
Credit value: 15
Assessment: written examination/s
One 2-hour written examination. Exercise sheets will be given out each week. Solutions handed in will be marked and difficulties discussed in the tutorial.

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