## Professional study programme

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## Course groups

Prikaži sve grupe na predmetu

## Course description

Primitive of a function. Indefinite integral. Methods of integration: the method of substitution, integration by parts. Integration of rational functions. Riemann integral. Newton-Leibniz formulae. Trapezoid rule. Simpsonâ€™s rule. , Length of the arc of a curve. Volume and surface of a solid of rotation. Problems in engineering referring to use of differential equations. Solution methods for differential equations. The existence theorem. Separation of variables. Homogenous differential equation. Linear differential equation of the first degree. Linear differential equation of the second degree with constant coefficients. Application of differential equations (simple harmonic oscillations, spring vibrations, damped vibrations, forced vibrations, simple electric networks). Numerical methods for solving differential equations. Series. Convergence of series. Criterion of convergence of the series with positive terms (comparison, d'Alembert, Cauchy's criterion). Leibniz's criterion for series with alternating signs. Convergence area. Power series. Convergence interval. Taylor and Mac Lauren series. Fourier series.

## Knowledge and skills acquired

Students will be introduced to fundamental concepts and simple applications of integral calculus, differential functions of series. 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 Jukić, D; Scitovski, R Matematika Osijek: Matematički odjel Osijek, 2000.

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

3. 3 B. Apsen Repetetitorij više matematike Tehnička knjiga, Zagreb, 2000.

Pretraži literaturu na: 1. 1 R. Scitovski, D. Jukić Matematika Matematički odjel, Osijek, 2001.

2. 2 P. Javor Matematička analiza Školska knjiga,Zagreb, 2000.

## 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. express and analyse the results of differential and integral calculus of a function of one variable

2. for a given mathematical problem, create an integral, solve it and interpret the solution

3. create a procedure by which we define the surface, arc length and the volume of the body

4. compare a differential equation with the basic types of differential equations and create a general solution

5. analyse the given series, compare it with known series, and examine and determine convergence

Aktivnosti studenta: Vidi tablicu aktivnosti