# Mathematics III

## Course description

Differential geometry (curves, surfaces in three-dimensional Euclidean space). Multiple integral (parameter-dependent integral, double and triple integral). Vector analysis (gradient, divergence, curl, nabla operator). Line and surface integrals (Green’s theorem, divergence theorem of Gauss, Stokes’s theorem). Complex analysis (complex analytic functions, elementary complex functions, complex integration, Laurent series, theory of residues).

## Objectives and competences

To upgrade the basic concepts of mathematical analysis, procedures, and laws. Further develop analytical thinking, careful and exact mathematical reasoning as well as other building blocks of science/mathematics/engineering literacy. To upgrade the knowledge of the software for symbolic computations (e.g., Mathematica).

## Learning and teaching methods

Lectures, tutorials, laboratory tutorials and homework assignments. 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 differential geometry and mathematical analysis, including vector and complex analysis,
• compute basic multiple, line and surface integrals,
• identify and understand problems in differently structured environments/contexts, carry out independent research,
• identify, analyse and use mathematical and ICT tools to solve natural science and engineering authentic problems,
• appropriately display/communicate and critically evaluate the solution procedure and the obtained results,
• master exactness, consistency and diligence in communication, thinking and work,
• demonstrate an appropriate attitude towards engineering practice and science.

## Reference nosilca

Gregor Dolinar

1. DOLINAR, Gregor, KUZMA, Bojan, MAROVT, Janko, POON, Edward. Spectrum preservers revisited. Journal of mathematical analysis and applications. [Print ed.]. Sep. 2020, vol. 489, no. 1, art. 124144 (13 str.). ISSN 0022-247X.

2. DOLINAR, Gregor, HALICIOGLU, Sait, HARMANCI, Abdullah, KUZMA, Bojan, MAROVT, Janko, UNGOR, Burcu. Preservers of the left-star and right-star partial orders. Linear Algebra and its Applications. [Print ed.]. Feb. 2020, vol. 587, str. 70-91. ISSN 0024-3795.

3. DOLINAR, Gregor, KUZMA, Bojan, MAROVT, Janko, UNGOR, Burcu. Properties of core-EP order in rings with involution. Frontiers of Mathematics in China. 2019, no. 4, vol. 14, str. 715-736. ISSN 1673-3452.

4. DOLINAR, Gregor, GUTERMAN, Aleksandr Èmilevič, KUZMA, Bojan, MARKOVA, Olga. Extremal generalized centralizers in matrix algebras. Communications in algebra. 2018, vol. 46, no. 7, str. 3147-3154. ISSN 0092-7872.

5. CRUZ, Henrique F. da, DOLINAR, Gregor, FERNANDES, Rosário, KUZMA, Bojan. Maximal doubly stochastic matrix centralizers. Linear Algebra and its Applications. [Print ed.]. 2017, vol. 532, str. 387-396. ISSN 0024-3795.

Melita Hajdinjak

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, G. Dolinar: Matematika III, zapiski predavanj, https://e.fe.uni-lj.si, 2021.
2. G. Tomšič, T. Slivnik: Matematika III,  Založba FE, Ljubljana, 2001.
3. R. Sperb, Analysis II, vdf Hochschulverlag, ETH Zürich, 2011.
4. E. Kreyszig: Advanced engineering mathematics, John Wiley & Sons, 2006
5. G. B. Thomas: Thomas' Calculus, Pearson Education, 2005
6. T. Žitko: Zbirka nalog iz Matematike III, Založba FE, 2002.
7. G. Dolinar: Rešene naloge iz Matematike III, Založba FE in FRI, Ljubljana, 2005.
8. Spletna učilnica eFE https://e.fe.uni-lj.si

## Bodi na tekočem

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