1. komponenta

Lecture type	Total
Lectures	45
Exercises	30

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

COURSE AIMS AND OBJECTIVES:
To learn the basics of vector algebra in space and analytic geometry in plane and space. With this course, we expand the first-year students' knowledge of analytic geometry and vector calculus, and we set the foundations on which the courses Linear algebra 1 and 2 build abstract concepts such as algebraic structures (group, vector space), operators etc. The terms related to curves, surfaces and geometric transformations are introduced from an analytical point of view, which is an introduction to geometry courses in the higher years of study, where these terms will be studied from the point of view of synthetic geometry.

COURSE DESCRIPTION AND SYLLABUS:
1-3) Classical vector algebra in V2 and V3. Directed line segments. Vectors. Length, orientation, and direction of vectors. Addition of vectors. Multiplication of a vector by a scalar. Structure of spaces V2 and V3. Linear dependence and independence of vectors. Basis of spaces V2 and V3. Coordinatization.
4) Dot product in V2 and V3 and its properties. Orthonormal bases. Coordinate representation of dot product.
5-6) Cross product and scalar triple product in V3 and their properties. Coordinate representation of cross product and scalar triple product.
7-9) Elements of analytic geometry in E3. Coordinate system on a straight line, in plane and space. Distance from a point to a plane. Diverse types of plane equation. Angle between two planes. Analytic representations of line. Angle between two lines. Angle between line and plane. Distance from a point to a line. Common perpendicular and shortest distance between two lines.
10-12) Polar coordinate system in plane. Second-degree curves in plane and their analytic representation. Equations of their tangent lines. Basic results on conics and their Pappus-Bošković characterisation.
13-14) Geometric transformations in R2 (axial and central symmetry, rotation, translation, homothety). Expressing geometric transformations in terms of coordinates and in matrix notation. Composition of transformations. Classification of second-degree curves.
15) Other coordinate systems in space. Geometric transformations in R3 (axial, central and plane symmetry, rotation around line, homothety, orthogonal projection on a plane, orthogonal projection on a line, translation). Second-degree surfaces in space.

1. Analitička geometrija (skripta), Ž. M. Šipuš, M. Bombardelli, PMF-MO, Zagreb, 2016.
2. Linearna algebra, K. Horvatić, Golden marketing - Tehnička knjiga, Zagreb, 2003.
3. Elementarna matematika 2, B. Pavković, D. Veljan, Školska knjiga, Zagreb, 1994.
4. Zbirka zadataka iz linearne algebre s rješenjima, N. Bakić, A. Milas, PMF - Matematički odsjek i Hrvatsko matematičko društvo, Zagreb, 1995.

Mandatory course - Regular study - Mathematics and Physics Education