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Euclidean spaces

Code: 33453
ECTS: 5.0
Lecturers in charge: izv. prof. dr. sc. Zrinka Franušić - Lectures
Lecturers: Ana Kontrec - Exercises
Borja Rukavina - Exercises
English level:

1,0,0

All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.
Load:

1. komponenta

Lecture typeTotal
Lectures 30
Exercises 30
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
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.
Literature:
Prerequisit for:
Enrollment :
Passed : Linear algebra 2
5. semester
Izborni predmet 1, 2 - Mandatory studij - Mathematics

6. semester Not active
Izborni predmet 1, 2 - Mandatory studij - Mathematics
Consultations schedule: