MATS195 Differential Geometry of Surfaces (4 cr)
Study level:
Advanced studies
Grading scale:
0-5
Language:
English
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2017-2018, 2018-2019, 2019-2020
Description
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’ Theorema egregium. Possibly also geodesics and the Gauss-Bonnet theorem.
Completion methods
Course exam and exercises or just a final exam.
Assessment details
The course is evaluated based on the course exam and exercise points
or just on the final exam.
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’ Theorema egregium
- 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’ Theorema egregium
Additional information
28h lectures, and exercises
Description of prerequisites
Elementary Differential Geometry
Study materials
M. Abate, F. Tovena: Curves and Surfaces, Chapters 3 & 4 (at least)
Literature
- M. Abate, F. Tovena: Curves and Surfaces, Springer-Verlag Mailand, 2012; ISBN: 978-88-470-1940-9
Completion methods
Method 1
Select all marked parts
Parts of the completion methods
x
Unpublished assessment item