MATS195 Differential Geometry of Surfaces (4 cr)
Learning outcomes
After the completion of the course the student
- can examine the properties of surfaces using different expressions for surfaces
- knows the first fundamental form of surfaces
- can determine areas and various curvatures of surfaces
- knows the contents and the significance Gauss鈥� Theorema egregium
Study methods
Course exam and exercises or just a final exam.
Content
Basic theory of surfaces, for instance: different ways to define and express surfaces, tangents and derivations, the first fundamental form, area and different notions of curvature, Gauss鈥� Theorema egregium. Possibly also geodesics and the Gauss-Bonnet theorem.
Further information
28h lectures, and exercises
Materials
M. Abate, F. Tovena: Curves and Surfaces, Chapters 3 & 4 (at least)
Literature:
| ISBN-number | Author, year of publication, title, publisher |
|---|---|
| 978-88-470-1940-9 | M. Abate, F. Tovena: Curves and Surfaces, Springer-Verlag Mailand, 2012 |
Assessment criteria
The course is evaluated based on the course exam and exercise points
or just on the final exam.
Prerequisites
Elementary Differential Geometry