COURSE GOALS: To provide students with a good understanding of the concepts and methods of linear algebra, such as the three dimensional vector space, analytic geometry in the space, and matrices.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
2.APPLYING KNOWLEDGE AND UNDERSTANDING
2.3. recognize and follow the logic of arguments, evaluate the adequacy of arguments and construct well supported arguments
2.4. use mathematical methods to solve standard physics problems
4. COMMUNICATION SKILLS
4.2. present complex ideas clearly and concisely
5. LEARNING SKILLS
5.1. search for and use professional literature as well as any other sources of relevant information
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
Upon passing the course, the student will be able to:
1. Perform the basic operations with vectors in the three dimensional space (addition, multiplication by scalars, dot product, cross product).
2. Find a representation of a vector with respect to various bases.
3. Use basic techniques of analytic geometry in the space; in particular, find equations of lines and planes and determine their mutual positions.
4. Define and explain basic concepts related to matrices.
5. Perform the basic matrix operations (addition, multiplication by scalars, matrix multiplication).
6. Calculate the determinant and the inverse of a matrix.
Vectors in three dimensions. Linear independence of vectors. Bases. Operations with vectors. Analytic geometry in space. Lines and planes in space. Matrices and determinants. Inverse of a matrix.
REQUIREMENTS FOR STUDENTS:
Students have to attend lectures and exercises, do homework, and solve 50% of the written exams.
GRADING AND ASSESSING THE WORK OF STUDENTS:
There are two written exams during the semester. The students who solve less that 20% of the written exams fail the course. The students who solve between 20% and 44% of the written exams have to retake exam, while those who solve more than 45% of the written exams take the oral exam. In order to pass the course, students need to pass both the written and oral exams. Thereby, 50% of the grade is carried by the results of the written exams and 50% by the results of the final oral exam.
- K. Horvatić, Linearna algebra 1 i 2, skripta, PMF-Matematički odjel, Zagreb, 1995.
- Lj. Arambašić, Matematika 3, nastavni materijali postavljeni na web stranici http://web.math.pmf.unizg.hr/~ljsekul/nastava/matematika3-w.pdf
- N. Elezović, A. Aglić, Linearna algebra, zbirka zadataka, Element, Zagreb, 1995.
- N. Bakić, A. Milas, Zbirka zadataka iz linearne algebre s rješenjima, skripta, PMF-Matematički odjel, Zagreb, 1995.
- L. Čaklović, Zbirka zadataka iz linearne algebre, Školska knjiga, Zagreb, 1985.
- V. Devide, Riješeni zadaci iz više matematike, Svezak I, Školska knjiga, Zagreb, 1989.
- S. Kurepa, Kvadratne matrice drugog i trećeg reda, Školska knjiga, Zagreb, 1979.
- S. Kurepa, Uvod u linearnu algebru, Školska knjiga, Zagreb, 1975.
- V.P. Minorski, Zbirka zadataka više matematike, Tehnička knjiga, Zagreb, 1972.
- I.V. Proskuryakov, Problems in Linear Algebra, Mir, Publishers, Moscow, 1978