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


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    Hours & Credits

  • UK Credits

  • Recommended U.S. Semester Credits
  • Recommended U.S. Quarter Units
  • 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.
    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.
    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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