Course title  Geometry  Exercises 

Course code  MU/01907 
Organizational form of instruction  Lesson 
Level of course  Bachelor 
Year of study  not specified 
Semester  Winter 
Number of ECTS credits  1 
Language of instruction  Czech 
Status of course  Compulsory, Compulsoryoptional 
Form of instruction  Facetoface 
Work placements  This is not an internship 
Recommended optional programme components  None 
Course availability  The course is available to visiting students 
Lecturer(s) 


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, FrenetSerret 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, GaussWeingarten equations; parallel displacement, geodesics; principal curvatures. Applications in cartography and physics.

Learning activities and teaching methods 
unspecified 
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 (2F)  Mathematics courses  2  Winter 
Faculty of Philosophy and Science in Opava  Theoretical Physics (2)  Physics courses    Winter 
Mathematical Institute in Opava  Mathematical Analysis (1IVT)  Mathematics courses  2  Winter 
Mathematical Institute in Opava  Mathematics (1IVT)  Mathematics courses  2  Winter 