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| Detailed information |
| Original study plan |
Master's programme Computational Mathematics 2025W |
| Learning Outcomes |
Competences |
| Students are familiar with basic differential geometric knowledge and with fundamental proof and computational techniques of differential geometry, which are assumed to be known in more advanced courses.
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| Skills |
Knowledge |
- use various descriptions of curves, surfaces and manifolds;
- analyze differential geometric properties of curves, surfaces and curves on surfaces;
- re-derive proofs of classical theorems of differential geometry;
- apply tensor calculus to investigate the properties of surfaces
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Frenet formulas and curvatures for curves in spaces of arbitrary dimension;
Surfaces and two-dimensional manifolds, theory of surface metrics and basic concepts of tensor calculus; basic concepts of the theory of surface curvature
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| Criteria for evaluation |
Exam
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| Methods |
Lecture
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| Language |
English |
| Study material |
- E. Kreyszig, Differential Geometry, Dover, 1990;
- M. DoCarmo, Differentialgeometrie von Kurven und Flächen, Vieweg;
- V. Wünsch, Differentialgeometrie - Kurven und Flächen, Wissenschaftsverlag Thüringen, 2012
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| Changing subject? |
No |
| Further information |
Necessary previous knowledge: Basic lectures in mathematics
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| Earlier variants |
They also cover the requirements of the curriculum (from - to)
402MMPHDGEV22: VO Differential Geometry (2022W-2023S)
TMAPAVODGEO: VO Differential geometry (2003S-2022S)
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