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.
|Paper title||Geometry of Curves and Surfaces|
|Teaching period||Semester 2 (On campus)|
|Domestic Tuition Fees (NZD)||$955.05|
|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