Course: Geometry

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Course title Geometry
Course code MU/01007
Organizational form of instruction Lecture
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 3
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
  • MARVAN Michal, doc. RNDr. CSc.
  • BARAN Hynek, RNDr. Ph.D.
Course content
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.

Learning activities and teaching methods
Recommended literature

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Mathematics (2-F) Mathematics courses 2 Winter
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 2 Winter
Mathematical Institute in Opava Mathematics (1-IVT) Mathematics courses 2 Winter