Course title  Analytic Geometry I 

Course code  MU/05085 
Organizational form of instruction  Lecture + Lesson 
Level of course  Bachelor 
Year of study  not specified 
Semester  Winter 
Number of ECTS credits  6 
Language of instruction  Czech 
Status of course  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 spaces. Linear subspaces, their parametric expression and expression in equations. Mutual positions of subspaces. Intersection and span of subspaces. Line orderings. Parallelism. Transversal of skew lines. Orientation. Halflines, halfspaces. Coordinate transformations in affine space. Linear forms. Metric spaces, examples. Euclidean space. Center of a pair of points. Inner product. Orthogonality of vectors, directions and subspaces. Orthogonal complement. Pseudoinner product. Distance of subspaces. Axis of skew lines. Linear forms in Euclidean space. Coordinate transformations in Euclidean space. Definition of the angle. Angles of halflines, lines, a line and a subspace. Projective extension of Euclidean space. Homogeneous coordinates. Double ratio.

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  Mathematical Analysis (1IVT)  Mathematics courses  3  Winter 
Mathematical Institute in Opava  Mathematics (1IVT)  Mathematics courses  3  Winter 
Mathematical Institute in Opava  Mathematics (2F)  Mathematics courses  3  Winter 