1. komponenta

Lecture type	Total
Lectures	30
Exercises	30

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES: Give an axiomatic approach to the notions of affine and euclidean spaces as generalizations of standard three-dimensional space. Introduce all fundamental notions and prove corresponding theorems.

COURSE DESCRIPTION AND SYLLABUS:
1. Definitions of affine and euclidean spaces. Examples. Elementary properties.
2. Planes in affine space (affine subspaces). Parallelism of the planes.
3. Intersection of the planes. Sum of the planes.
4. Coordinate system in an affine space.
5. Equations of a plane, hyperplane and straight line.
6. Convex sets. Halfspaces.
7. Parallelotope. Simplex.
8. Affine transformations. Affine group of an affine space.
9. Analytic representation of an affine transformation.
10. Euclidean space. Cartesian (rectangular) coordinates.
11. Distance. Angle.
12. Volume.
13. Analytic geometry of an euclidean space.
14. Isometry. Isometric operators.
15. Subgroups of the group of isometries.

Enrollment :
Passed : Linear algebra 2

Izborni predmet 1, 2 - Mandatory studij - Mathematics

Izborni predmet 1, 2 - Mandatory studij - Mathematics