# Mathematics I

## Course description

Number systems (positive integers, rational numbers, real numbers, complex numbers). Sequences (accumulation point, limit, boundedness). Series (convergence, convergence tests, harmonic series, alternating series). Functions of one real variable (domain of definition, image, oddness and evenness, injectivity, surjectivity, bijectivity, composition, inverse function, elementary functions, limit , continuity). Derivative of a function (derivation rules, geometric interpretation, differential, applications). Integral of a function (indefinite integral, definite integral, applications of definite integral).

## Objectives and competences

To master the basic concepts of mathematical analysis and to be able to better understand them. To develop analytical thinking and careful and exact mathematical reasoning as well as other building blocks of science/mathematics/engineering literacy.

## Learning and teaching methods

Lectures, tutorials, and individualized homework. Collective analysis, interpretation, and solving of technical problems.

## Intended learning outcomes

After successful completion of the course, students should be able to:

• solve basic problems of mathematical analysis, including sequences, series, real functions, derivatives and integrals,
• compute the derivatives of elementary functions and integrals of some classes of functions,
• identify and understand technical/engineering problems in differently structured environments/contexts,
• identify, analyse and use mathematical tools to solve simple natural science and engineering authentic problems,
• appropriately display/communicate and critically evaluate the solution procedure and the obtained results,
• demonstrate an appropriate attitude towards engineering practice and science.

## Reference nosilca

1. HAJDINJAK, Melita. Functions with linear price elasticity for forecasting demand and supply. The B.E. journal of theoretical economics. Jan. 2021, vol. 21, iss. 1, str. 149-168, ilustr. ISSN 1935-1704.

2. HAJDINJAK, Melita, MILJAVEC, Damijan. Analytical calculation of the magnetic field distribution in slotless brushless machines with U-shaped interior permanent magnets. IEEE transactions on industrial electronics. [Print ed.]. Aug. 2020, vol. 67, iss. 8, str. 6721 – 6731, ilustr. ISSN 0278-0046.

3. SULIĆ KENK, Vildana, MANDELJC, Rok, KOVAČIČ, Stanislav, KRISTAN, Matej, HAJDINJAK, Melita, PERŠ, Janez. Visual re-identification across large, distributed camera networks. Image and vision computing, ISSN 0262-8856, Feb. 2015, vol. 34, str. 11-26.

4. VODOPIVEC, Samo, HAJDINJAK, Melita, BEŠTER, Janez, KOS, Andrej. Vehicle interconnection metric and clustering protocol for improved connectivity in vehicular ad hoc networks. EURASIP Journal on wireless communications and networking, ISSN 1687-1499, 2014, 2014, 170, str. 1-14.

5. RUGELJ, Miha, SEDLAR, Urban, VOLK, Mojca, STERLE, Janez, HAJDINJAK, Melita, KOS, Andrej. Novel cross-layer QoE-aware radio resource allocation algorithms in multiuser OFDMA systems. IEEE transactions on communications, ISSN 0090-6778, Sep. 2014, vol. 62, no. 9, str. 3196-3208.

## Study materials

1. M. Hajdinjak, Matematika 1 na programu aplikativna elektrotehnika, 2. izdaja, Založba FE in FRI, 2019.

2. G. Dolinar, Matematika 1, Založba FE in FRI, 2010.

3. G. Tomšič, B. Orel, N. Mramor Kosta: Matematika I,  Založba FE in FRI, Ljubljana, 2004.

4. G. B. Thomas: Thomas’ Calculus, Pearson Education, 2005.

5. B. Jurčič-Zlobec, N. Mramor Kosta: Zbirka nalog iz Matematike I, Založba FE in FRI, 2009.

6. G. Dolinar, U. Demšar: Rešene naloge iz Matematike I za VSP, Založba FE in FRI, 2004.

Spletna učilnica eFE https://e.fe.uni-lj.si

## Bodi na tekočem

Univerza v Ljubljani, Fakulteta za elektrotehniko, Tržaška cesta 25, 1000 Ljubljana