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    An introduction to differential geometry with a focus on the structure of two-dimensional surfaces.

    This paper provides the necessary tools to describe two-dimensional surfaces in many applications, such as modelling air flow around cars, architecture, etc.

    About this paper

    Paper title Geometry of Curves and Surfaces
    Subject Mathematics
    EFTS 0.15
    Points 18 points
    Teaching period Not offered in 2024 (On campus)
    Domestic Tuition Fees ( NZD ) $981.75
    International Tuition Fees Tuition Fees for international students are elsewhere on this website.
    MATH 202 and MATH 203
    Schedule C
    Arts and Music, Science
    This paper is particularly relevant to Mathematics and Physics majors.

    Teaching staff

    Professor Jörg Frauendiener

    Paper Structure
    Main topics:
    • Curves in the plane and in space (parametrised curves, arc length, Frenet-Serret equations)
    • Regular surfaces (regular values, functions on surfaces, first and second fundamental forms)
    • Intrinsic geometry of surfaces (the Gauss theorem, parallel transport and geodesics, Gauss Bonnet and applications)
    Teaching Arrangements
    Three lectures and one tutorial per week.
    Andrew Pressley, Elementary Differential Geometry, Springer Verlag (this book is freely downloadable in electronic form from Springer Verlag).
    Graduate Attributes Emphasised
    Critical thinking.
    View more information about Otago's graduate attributes.
    Learning Outcomes
    • Demonstrate in-depth understanding of geometric concepts
    • Capability to apply them in real-world problems


    Not offered in 2024

    Teaching method
    This paper is taught On Campus
    Learning management system
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