Course: Analytic Geometry II

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Course title Analytic Geometry II
Course code MU/05086
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 6
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
Lecturer(s)
  • VOJČÁK Petr, RNDr. Ph.D.
  • SEDLÁŘ Vladimír, RNDr. CSc.
Course content
Affine maps. Group of affine maps. Fixed points and directions of affine maps. Basic affinities. Module of affinity, equiaffinity. Classification of affinities in the plane. Congruences of Euclidean space. Group of congruences. Reflection in a hyperplane. Symmetries in Euclidean space. Classification of congruences on a line, a plane and in three-dimensional Euclidean space. Similarities. Group of similarities. Classification of similarities in the plane. Conic sections. Basic metric theory of conics. Algebraic curves of second order. Central and non-central curves of second order. Diameters of curves of second order. Quadrics. Bilinear and quadratic forms. Classification of quadrics. Quadrics in three-dimensional space. Tangent planes of surfaces of second order.

Learning activities and teaching methods
unspecified
Recommended literature
  • J. Janyška, A. Sekaninová. Analytická teorie kuželoseček a kvadrik. Brno, 1996. ISBN 80-210-1435-0.
  • M. Sekanina. Analytická geometrie II. Praha, 1989.


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 Summer
Mathematical Institute in Opava Mathematics (2014-F) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematics (2-F) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematics (1-IVT) Mathematics courses 3 Summer