## Professional study programme

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## Course groups

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## Course description

Function. Graph of a function. Composite function. Inverse function. Elementary functions (polynomial, rational function, exponential and logarithmic function, power function, trigonometric and inverse trigonometric functions, hyperbolas and area functions). Sequences. Convergence of sequences. Basic theorems on convergence. Limits and continuity of functions. Asymptotes. Derivative of a function. Derivative as velocity. Derivative and the tangent. Differential. Derivatives of elementary functions. Rules of differentiation. Derivatives of composite functions. Higher derivatives. Basic theorems of differential calculus (Fermat's, Rolle's, Langrange's, Cauchy's theorem). Taylor's theorem. Approximation functions by a polynomial. Local extremes. Convexity, concavity and inflection points. Curvature. L'Hospital's rule. Methods for numerical solution of equations (direct and iterative methods). Vector as a class of directed line segments. Addition of vectors. Multiplication of a vector by a scalar. Vector space. Basis of a vector space. Scalar product. Vector product. System of linear equations. Gaussian elimination method. Matrix representation of a system of linear equations. Theorem of Kronecker-Capelli. A set of solutions to equation F(x,y)=0: circle, ellipse, parabola, hyperbola.

## Knowledge and skills acquired

Students will be introduced to fundamental concepts and simple applications of functions, differential and vector calculus as well as principles of solving a system of linear equations. They will also be trained and prepared for long-life learning and use of mathematical structures, relations and operations as application tools.

## Teaching methods

Students are obliged to attend both lectures and laboratory practice.

## 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 tests which replace the written examination. This ensures continuous assessment of studentsâ€™ work and knowledge.

## Obligatory literature

1. 1 R. Galić, M. Crnjac, I. Galić Matematika za stručne studije ETF Osijek i Veleučilište Požega.

2. 2 Demidović, B. P. Zadaci i riješeni primjeri iz više matematike s primjenom na tehničke nauke Zagreb: Tehnička knjiga, 2003.

Pretraži literaturu na: 1. 1 B. Apsen Repetetitorij više matematike Tehnička knjiga, Zagreb, 2000.

2. 2 R. Scitovski, D. Jukić Matematika Matematički odjel, Osijek, 2001.

## Examination methods

The final examination consists of the written and the oral part. Students can take the final examination after the completion of lectures and problem solving exercises.

## 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. define, classify and graphically draw elemental functions

2. compare and explain the features of elementary functions

3. create and analyse the derivative of the function

4. compare, calculate and create vectors, and evaluate and solve matrix tasks

5. analyse and determine equations of a line and plane in space

6. analyse and determine a solution to a system of linear equations

Aktivnosti studenta: Vidi tablicu aktivnosti