Overview
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 | Semester 2 (On campus) |
| Domestic Tuition Fees ( NZD ) | $1,103.10 |
| International Tuition Fees | Tuition Fees for international students are elsewhere on this website. |
- Prerequisite
- MATH 202 and MATH 203
- Schedule C
- Arts and Music, Science
- Eligibility
- This paper is particularly relevant to Mathematics and Physics majors.
- Contact
- Teaching staff
- 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.
- Textbooks
- 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
Overview
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 | 0.1500 |
| Points | 18 points |
| Teaching period | Semester 2 (On campus) |
| Domestic Tuition Fees | Tuition Fees for 2027 have not yet been set |
| International Tuition Fees | Tuition Fees for international students are elsewhere on this website. |
- Prerequisite
- MATH 202 and MATH 203
- Schedule C
- Arts and Music, Science
- Eligibility
This paper is particularly relevant to Mathematics and Physics majors.
- Contact
- Teaching staff
- 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.
- Textbooks
- Andrew Pressley. (2010). Elementary Differential Geometry (2nd ed.). 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.