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### Mathematics 4

 Code: 40790 ECTS: 7.0 Lecturers in charge: izv. prof. dr. sc. Maja Resman Lecturers: izv. prof. dr. sc. Maja Resman - Exercises Take exam: Studomat

### 1. komponenta

Lecture typeTotal
Lectures 45
Exercises 30
Description:
COURSE GOALS: To provide students with a good understanding of the concepts and methods of linear algebra, such as systems of linear equations, vector spaces and linear operators.
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. Understand basic concepts related to systems of linear equations.
2. Solve systems of linear equations by Gaussian elimination.
3. Find the inverse of a matrix by the Gauss-Jordan method.
4. Define and explain basic concepts related to vector spaces, and give some examples of vector spaces.
5. Define and explain basic concepts related to linear operators, and give some examples of linear operators.
6. Find the kernel, range, rank, and nullity of a linear operator.
7. Calculate eigenvalues and corresponding eigenvectors.

COURSE DESCRIPTION:
Systems of linear equations. Rank of a matrix. Vector spaces. Subspaces. Basis and dimension. Linear operators. Characteristic and minimal polynomials. Eigenvalues and eigenvectors.

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.
Literature:
1. K. Horvatić, Linearna algebra 1 i 2, skripta, PMF-Matematički odjel, Zagreb, 1995.
2. Lj. Arambašić, Matematika 4, nastavni materijali postavljeni na web stranici http://web.math.pmf.unizg.hr/~ljsekul/nastava/matematika4_w.pdf
3. N. Bakić, A. Milas, Zbirka zadataka iz linearne algebre s rješenjima, skripta, PMF-Matematički odjel, Zagreb, 1995.
4. L. Čaklović, Zbirka zadataka iz linearne algebre, Školska knjiga, Zagreb, 1985.
5. V. Devide, Riješeni zadaci iz više matematike, Svezak I, Školska knjiga, Zagreb, 1989.
6. N. Elezović, A. Aglić, Linearna algebra, zbirka zadataka, Element, Zagreb, 1995.
7. S. Kurepa, Kvadratne matrice drugog i trećeg reda, Školska knjiga, Zagreb, 1979.
8. S. Kurepa, Uvod u linearnu algebru, Školska knjiga, Zagreb, 1975.
9. V.P. Minorski, Zbirka zadataka više matematike, Tehnička knjiga, Zagreb, 1972.
10. I.V. Proskuryakov, Problems in Linear Algebra, Mir, Publishers, Moscow, 1978
Prerequisit for:
Enrollment :
Attended : Mathematics 3

Examination :
Passed : Mathematics 3
 4. semester Mandatory course - Regular study - Physics and Technology Education
Consultations schedule:

### Content

Link to the course web page: https://www.pmf.unizg.hr/phy/predmet/mat4