MATA235 Differential geometry of curves (4 cr)
Study level:
Intermediate studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2017-2018, 2018-2019, 2019-2020
Description
Content
Local and global properties of curves from the point of view of differential geometry. For instance: parametrization of curves, curvature and torsion of curves, the local canonical form, the Jordan curve theorem, isoperimetric inequality.
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 length and parametrization of curves
- masters the definitions of curvature and torsion and can apply these
- knows the local canonical form of curves
- knows the contents and the significance of the Jordan curve theorem and the isoperimetric inequality.
- can examine the length and parametrization of curves
- masters the definitions of curvature and torsion and can apply these
- knows the local canonical form of curves
- knows the contents and the significance of the Jordan curve theorem and the isoperimetric inequality.
Additional information
28h lectures, and exercises
Description of prerequisites
Vector Analysis 1 and 2
Study materials
M. Abate, F. Tovena: Curves and Surfaces, Chapters 1 & 2 (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Unpublished assessment item