1. komponenta

Lecture type	Total
Lectures	45
Exercises	30

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

COURSE AIMS AND OBJECTIVES: The main aim of this course is to systematize and expand the student knowledge on vectors algebra and analytic geometry. The students will be introduced to spaces of two and three-dimensional vectors on which they will consider basic conceptions related to operations on vector spaces, linear independence, basis, dimension, inner product etc. Those ideas will be given in the abstract form in the following courses such as Linear Algebra, Vector spaces etc. A systematic overview (analytic approach) of the second-degree curves in plane and the second-degree surfaces in space will be done. Students' knowledge about geometric transformations will be improved and systematized.

COURSE DESCRIPTION AND SYLLABUS:
1. Vector space V2 . Directed line segments. Vectors. Lenght, orientation and direction of vectors. Addition and multiplication by a number. Structure of V2. Linearly independent set of vectors. Basis. Coordinate system. Inner product.
2. Vector space V3 . Directed line segments. Vectors. Addition and multiplication by a number. Structure of V3. Linearly independent set of vectors. Basis. Coordinate system. Inner and outer product.
3. Analytic geometry in E3. Coordinate system on line, in plane and space. Distance from a point to a plane. Various types of plane equation. Angle between two planes. Straight line in space. Angle between two straight lines. Angle between line and plane. Distance from a point to a line. Common perpendicular of two lines. Second-degree curves in plane and space. Second-degree surfaces. Polar coordinates. Cylindric and spherical coordinates.
4. Geometric transformations. Geometric transformations in Euclidean plane and space. Composition of two or more transformations. Expressing a geometric transformation in term of coordinates and in matrix notation.

Mandatory course - Regular study - Mathematics Education