Third-Cycle Courses

Faculty of Engineering | Lund University

Details for the Course Syllabus for Course MATM13F valid from Autumn 2018

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  • The aim of the course is to give the graduate student good knowledge about important concepts for the mathematical description of smooth two dimensional surfaces in space.
  • Geometry for hypersurfaces in Euclidean spaces. The Gauss map, curvature, focal points, minimal surfaces, convex surfaces, the Gauss-Bonnet theorem in two dimensions.
Knowledge and Understanding
  • For a passing grade the doctoral student must
  • be able to account for basic concepts of differential geometry such as principal curvatures, Gaussian curvature, mean curvature and, geodesics.
    be able to explain how the principal curvatures in a point determine the local shape of the surface near the point.
    be able to explain how knowledge about how the Gaussian curvature varies over the surface gives information about the global form of the surface.
Competences and Skills
  • For a passing grade the doctoral student must
Judgement and Approach
  • For a passing grade the doctoral student must
Types of Instruction
  • Lectures
  • Seminars
Examination Formats
  • Written exam
  • Oral exam
  • Written assignments
  • Compulsory assignments may occur.
  • Failed, pass
Admission Requirements
  • At least 60 hp mathematics.
Assumed Prior Knowledge
  • Calculus in several variables including vector analysis in three dimensions.
Selection Criteria
  • Gudmundsson, S.: An Introduction to Gaussian Geometry. Centre for Mathematical Sciences, Lund University, 2017.
Further Information
Course code
  • MATM13F
Administrative Information
  •  -08-24
  • Professor Thomas Johansson

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