Undergraduate study programme

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Linear Algebra P101

ECTS 5 | P 30 | A 30 | L 0 | K 0 | ISVU 37100 | Academic year: 2017./2018.

Course groups

Prikaži sve grupe na predmetu

Course lecturers

KATIĆ ANITA, Lecturer
GALIĆ RADOSLAV, Lecturer

Course description

Elements of mathematical logic. Vector space V3. Operations on vectors. Linearly dependent and independent vectors. Vector projection. Base of a vector space. Coordinate system. Scalar, vector and triple product. Analytic geometry. Point, line, plane and mutual relations. Matrix and elementary transformations of matrices. Operations with matrices. Vector space of matrices. Determinant and its properties. Calculation of determinant value. Rank of a matrix. Regular matrices. Inverse matrices. Systems of linear equations. Discussion of solutions. Methods for solving systems of equations. n-dimensional vector space. Base and space dimension. Subspaces. Examples of vector space. Linear operator. Representation of a linear operator in a basis. Algebra. Minimum polynomial. Similarity of matrices. Eigenvalues and eigenvectors. Characteristic polynomial. Hamilton-Cayley theorem. Matrix diagonalisation. Scalar product. Norm. Unitary spaces. Orthogonality. Gramm-Schmidt orthogonalisation. Quadratic forms. Curves of second degree. Second degree surfaces.

Knowledge and skills acquired

Students are introduced to linear algebra calculus and algebraic structures fundamental to many other courses. Lectures and exercises will include basic terminology whose usage will be illustrated by various examples and tasks.

Teaching methods

Mandatory lectures and exercises.

Student requirements

Defined by the Student evaluation criteria of the Faculty of Electrical Engineering, Computer Science and Information Technology Osijek and paragraph 1.9

Monitoring of students

Defined by the Student evaluation criteria of the Faculty of Electrical Engineering, Computer Science and Information Technology Osijek and paragraph 1.9

Student assessment

During the semester, students can take several revision exams which replace the written exam. This ensures a continuous assessment of students’ work and knowledge.

Obligatory literature

1. Elezović, N; Aglić, A. Linearna algebra, zbirka zadataka. Zagreb: Element, 2001.

2. Lipschutz, Seymour. Linear algebra, Schaum's outlines, 1991.

3. K.Horvatić, Linearna algebra, PMF Matematički odjel, Zagreb,1995.


Pretraži literaturu na:

Recommended additional literature

1. S.Kurepa, Uvod u linearnu algebru, Školska knjiga, Zagreb,1990.

2. L.Čaklović, Zbirka zadataka iz linearne algebre, Školska knjiga, Zagreb 1979.

3. R.Galić, Osnive linearne algebre, ETF, Osijek, 1994.

4. N.Elezović, Linearna algebra, Element, Zagreb, 1995

5. N.Bakić, A.Milas, Zbirka zadataka iz linearne algebre, PMF Matematički odjel, Zagreb,1995.

ECTS credits

An ECTS credit value has been added according to calculation of time required for studying and successful course completion.

Examination methods

The final assessment consists of both the written and oral exam upon completion of lectures and exercises. During the semester, students can take several revision exams replacing the written exam.

Course assessment

Conducting university questionnaires on teachers (student-teacher relationship, transparency of assessment criteria, motivation for teaching, teaching clarity, etc.). Conducting Faculty surveys on courses (upon passing the exam, student self-assessment of the adopted learning outcomes and student workload in relation to the number of ECTS credits allocated to activities and courses as a whole).

Overview of course assesment

Learning outcomes
Upon successful completion of the course, students will be able to:

1. graphically construct a linear combination of vectors and select a computational operation from vector space V3 when solving problem tasks

2. define matrices and perform basic computational operations with matrices

3. for the given relationship between points, lines and planes in space, create equations which will result in the required object or relationship

4. for the given linear operator, create a kernel and an image, and if the domain and codomain are the same vector space, determine the minimal polynomial and diagonise the matrix

5. solve the system of linear equations by various methods and discuss solutions



Learning outcomes available only as desktop version    Export to Excel
Student's activity Workload ECTS (Workload/30) Learning outcomes
Upon successful completion of the course, students will be able to:
Teaching
method
Assessment method Points
Attendance
Lectures, Auditory exercises

60
ECTS
2
- define matrices and perform basic computational operations with matrices- for the given relationship between points, lines and planes in space, create equations which will result in the required object or relationship- for the given linear operator, create a kernel and an image, and if the domain and codomain are the same vector space, determine the minimal polynomial and diagonise the matrix- solve the system of linear equations by various methods and discuss solutionsLectures, Auditory exercises Attendance register. Mandatory attendance percentage is:
70%

This percentage defines the minimum workload for the activity. The maximum is defined by the study programme.
Min

0
Max

5
Practice – problem solving Workload
30
ECTS

1
- graphically construct a linear combination of vectors and select a computational operation from vector space V3 when solving problem tasks- define matrices and perform basic computational operations with matrices- for the given linear operator, create a kernel and an image, and if the domain and codomain are the same vector space, determine the minimal polynomial and diagonise the matrix- solve the system of linear equations by various methods and discuss solutionsMidterm exam Evaluation of (written) exercises Min

20
Max

40
Oral exam Workload
30
ECTS

1
- graphically construct a linear combination of vectors and select a computational operation from vector space V3 when solving problem tasks- define matrices and perform basic computational operations with matrices- for the given relationship between points, lines and planes in space, create equations which will result in the required object or relationship- for the given linear operator, create a kernel and an image, and if the domain and codomain are the same vector space, determine the minimal polynomial and diagonise the matrix- solve the system of linear equations by various methods and discuss solutionsOral exam Assessment of student's answers Min

25
Max

50
Homework Workload
30
ECTS

1
- graphically construct a linear combination of vectors and select a computational operation from vector space V3 when solving problem tasks- define matrices and perform basic computational operations with matrices- for the given linear operator, create a kernel and an image, and if the domain and codomain are the same vector space, determine the minimal polynomial and diagonise the matrix- solve the system of linear equations by various methods and discuss solutionsHomework Questions related to the subject contents Min

0
Max

5
Σ Activities Σ Workload
150
Σ ECTS
5
Σ Max
100