Mathematics IV

Course description

Integral transformations (Fourier transformation, Laplace transformation). Special functions (Gamma function, Beta function, Bessel functions). Partial differential equations wave equation, heat equation, Laplace equation). Calculus of variations (Euler equation). The finite element method.

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:

• describe integral transformations, use some special functions and apply calculus of variations,
• solve some of the most important partial differential equations,
• 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: Matematika IV, zapiski predavanj, https://e.fe.uni-lj.si, 2021.
2. G. Tomšič, T. Slivnik: Matematika IV,  Založba FE, Ljubljana, 2004.
3. E. Kreyszig: Advanced engineering mathematics, John Wiley & Sons, 2006.
4. R. L. Burden, J. D. Faires: Numerical Analysis, 9th Edition, Brooks/Cole, 2011.
5. L. Komzsik: Applied Calculus of Variations for Engineers, CRC Press, Taylor & Francis Group, Boca Raton, 2009.
6. T. Žitko: Zbirka nalog iz Matematike IV, Založba FE, Ljubljana, 2016.
7. Spletna učilnica eFE https://e.fe.uni-lj.si

Bodi na tekočem

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