MU:MU05086 Analytic Geometry II - Course Information

MU05086 Analytic Geometry II

Mathematical Institute in Opava
Summer 2017

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: zk (examination).

Teacher(s)

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

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.

Literature

recommended literature

J. Janyška, A. Sekaninová. Analytická teorie kuželoseček a kvadrik. Brno, 1996. ISBN 80-210-1435-0. info
M. Sekanina. Analytická geometrie II. Praha, 1989. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.