MU:MU05086 Analytic Geometry II - Course Information
MU05086 Analytic Geometry II
Mathematical Institute in OpavaSummer 2016
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- RNDr. Petr Vojčák, Ph.D. (lecturer)
RNDr. Petr Vojčák, Ph.D. (seminar tutor) - Guaranteed by
- RNDr. Petr Vojčák, Ph.D.
Mathematical Institute in Opava - Prerequisites (in Czech)
- MU05083 Analytic Geometry || MU05084 Analytic Geometry I || MU05085 Analytic Geometry I
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Mathematical Analysis (programme MU, M1101)
- Mathematics (programme MU, B1101)
- Secondary School Teacher Traning in Physics and Mathematics (programme FPF, M1701 Fyz)
- Course objectives (in Czech)
- Obsahem prednášek je analytický přístup ke studiu lineárnich zobrazení, kuželoseček a kvadrik v projektivní, afinní a eukleidovské rovině a prostoru.
- Syllabus
- 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.
- 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.
- Literature
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
- Enrolment Statistics (Summer 2016, recent)
- Permalink: https://is.slu.cz/course/sumu/summer2016/MU05086