MU:MU01017 Geometry - Course Information
MU01017 Geometry
Mathematical Institute in OpavaWinter 2017
- Extent and Intensity
- 2/0/0. 4 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Hynek Baran, Ph.D. (lecturer)
- Guaranteed by
- doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava - Prerequisites (in Czech)
- MU01002 Mathematical Analysis II && MU01917 Geometry - Exercises && MU01016 Algebra II
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Applied Mathematics (programme MU, B1101)
- Mathematics (programme MU, B1101)
- Course objectives
- Covering part of the requirements of the Comprehensive Exam in Mathematics, the course introduces basic concepts, methods, and applications of geometry of subspaces, curves and subvarieties in Euclidean space.
- Syllabus
- Affine and Euclidean spaces and subspaces, affine maps and isometries, affine and Cartesian coordinates.
Distance and inclination of subspaces in Euclidean space, the volume of a parallelepiped.
Applications in planimetry, stereometry, and coding theory.
Curves in Euclidean space, parameterization; Frenet frame, curvatures, Frenet--Serret equations; evolutes and involutes.
Subvartieties in Euclidean space, regular parameterization, tangent space, directional derivative, the first fundamental form, vector field, Lie bracket.
Hypersurfaces in Euclidean space, normal vector, covariant derivative, the second fundamental form, Gauss--Weingarten equations; parallel displacement, geodesics; principal curvatures.
Applications in cartography and physics.
- Affine and Euclidean spaces and subspaces, affine maps and isometries, affine and Cartesian coordinates.
- Literature
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
- Teacher's information
- A written examination followed by an oral examination.
- Enrolment Statistics (Winter 2017, recent)
- Permalink: https://is.slu.cz/course/sumu/winter2017/MU01017