## Undergraduate study programme

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## Course groups

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## Course description

Real functions of several real variables. Level curves and level surfaces. Limits and continuity. Partial derivatives and differential. Equation of tangent plane to a surface. Partial derivatives of composite functions and implicit functions. Partial derivatives and differentials of higher orders. Taylor's formula for functions of several variables. Extrema and conditional extrema of functions of several variables. Double and triple integrals - basic concepts, calculation and applications. Line integrals (of the first and of the second kind) â€“ definition, properties, calculation and applications. Vector functions of several variables. Scalar and vector field. Gradient of a scalar field; divergence of a vector field; curl of a vector field; applications. Complex functions of a complex variable. Derivative. Cauchy-Riemann equations. Integral of function of a complex variable. Cauchy theorem and integral formula. Taylor and Laurent series. Singularities. Residues.

## Knowledge and skills acquired

Students are introduced to the basic ideas and methods of functions of several variables and functions of a complex variable as the basis for other courses. The emphasis will be put on applications and basic concepts will be analysed in an informal way. During exercises, students should acquire certain techniques and be trained for solving specific problems.

## Teaching methods

Mandatory lectures and auditory 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 studentsâ€™ work and knowledge. The final exam consists of the written and oral part.

## Obligatory literature

1. 1 Javor, P. Matematička analiza II Zagreb: Element, 2000.

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

3. 3 H. Kraljević, S. Kurepa Matematička analiza 4/1 (funkcija kompleksne varijable) Tehnička knjiga, Zagreb, 1986.

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## Recommended additional literature

1. 1 M. Krasnov et al. Mathematical Analysis for Engineers – Vol. 1, & ibid. Vol. 2 Mir Publishers, Moscow, 1990.

2. 2 S. Kurepa Matematička analiza 3 (funkcije više varijabli) Tehnička knjiga, Zagreb, 1979.

3. 3 R. Galić Funkcije kompleksne varijable – za studente tehničkih fakulteta Osijek, Elektrotehnički fakultet, 1994.

4. 4 N. Elezović, D. Petrizio Funkcije kompleksne varijable: zbirka zadataka Element, Zagreb, 1994.

## 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. discuss functions of several variables and graphically illustrate the functions of two variables, and understand the concept of multidimensional space

2. calculate partial derivatives and differentials of the first and higher orders for functions of several variables

3. calculate function extrema of several variables and conditional extrema

4. define double and triple integrals, discuss them and calculate examples and applications

5. calculate curve integrals of the first and second kind and apply them in exercises

6. use concepts of scalar and vector fields, and basic vector calculus in engineering theory and application; understand the concept of complex functions of a complex variable

Aktivnosti studenta: Vidi tablicu aktivnosti