## Differential year

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## Course groups

Prikaži sve grupe na predmetu

## Course description

Vector. space. Base and dimension of the vector space. Subspaces. Linear operator. Representation of a linear operator in a base. Algebra. Minimal polynomial. Similarity of matrices. Eigenvalues and eigenvectors of a matrix. Concept and properties of the Riemann integral. Integrability of monotonic and continuous functions. The mean value theorem for integral of the continuous function. Real-valued function of n real variables. Level curves and level surfaces. Limits and continuity. Partial derivatives and total differential. Equation of a tangent plane and a normal line to the surface. Higher order partial derivatives and differential. Extreme values of a function of n variables. Double and triple integrals. Line integrals. Application of a double integral. Vector functions of n variables. Scalar and vector field. Gradient of a scalar field, divergence of a vector field, curl of a vector field. Function of a comlex variable. Cauchy-Riemann equations. Integral of a function of a complex variable. Cauchy's theorem and integral formula

## Knowledge and skills acquired

Teach students those parts of courses Linear Algebra, Mathematics II and Mathematics III they had not studied during their professional study programme.

## Teaching methods

Auditory exercises and lectures.

## 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

Continuous assessment through problem solving tasks during class.

## Obligatory literature

1. 1 Elezović, N; Aglić A. Linearna algebra, zbirka zadataka Zagreb: Element, 1995.

2. 2 P. Javor Matematička analiza II Element, Zagreb, 2000.

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

4. 4 S. Kurepa Matematička analiza 3 Tehnička knjiga, 1979, Zagreb;

5. 5 Apsen, B. Riješeni zadaci iz više matematike 3 Zagreb: Tehnička knjiga, 1989.

6. 6 N.Elezović Linearna algebra Element, Zagreb, 1995.

7. 7 H. Kraljević, S. Kurepa Matematička analiza 4/1 (funkcija kompleksne varijable) Tehnička knjiga, Zagreb, 1986.

Pretraži literaturu na:

1. 1 A. Aglić, N. Elezović Linearna algebra, zbirka zadataka Element, Zagreb, 1995.

2. 2 B.P. Demidovič Zadaci i riješeni primjeri iz više matematike s primjenom na tehničke nauke Tehnička knjiga, Zagreb, 1986.

## Examination methods

Written and oral part of examination

## 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. investigate whether the given set with the given binary operations is a vector space and specify the base and dimension

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

3. for the given function of two variables, create a graph of the function of two variables and discuss its domain

4. for the given function of n variables, create its differential and apply it when solving specific mathematical problems

5. for the given area and volume problem, create a multiple integral to solve the problem

6. for the given area problem, construct a suitable line integral and solve it

7. define the function of a complex variable, determine its derivation, and calculate the integral

Aktivnosti studenta: Vidi tablicu aktivnosti