Course: Analytic Geometry I

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Course title Analytic Geometry I
Course code MU/05084
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory-optional
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
  • VOJČÁK Petr, RNDr. Ph.D.
  • SEDLÁŘ Vladimír, RNDr. CSc.
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. Half-lines, half-spaces. 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. Pseudo-inner product. Distance of subspaces. Axis of skew lines. Linear forms in Euclidean space. Coordinate transformations in Euclidean space. Definition of the angle. Angles of half-lines, lines, a line and a subspace. Projective extension of Euclidean space. Homogeneous coordinates. Double ratio.

Learning activities and teaching methods
Recommended literature
  • M. Sekanina a kol. Analytická geometrie I. Praha, 1986.
  • P. Horák, J. Janyška. Analytická geometrie. Brno, 1997.

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 (2014-IVT) Mathematics courses 3 Winter
Mathematical Institute in Opava Mathematics (2014-F) Mathematics courses 3 Winter