MU:MU05084 Analytic Geometry I - Course Information

MU05084 Analytic Geometry I

Mathematical Institute in Opava
Winter 2015

Extent and Intensity

2/2/0. 4 credit(s). Type of Completion: z (credit).

Teacher(s)

Guaranteed by

RNDr. Petr Vojčák, Ph.D.
Mathematical Institute in Opava

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)

Předmět slouží k seznámení se základy analytické geometrie. Obsahem seminářů je řešení příkladů k jednotlivým tématům látky probírané na přednáškách.

Syllabus

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.

Literature

recommended literature

Language of instruction

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.