# 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 problems in differently structured environments/contexts,
• identify, analyse and use mathematical tools to solve natural science and engineering authentic problems,
• appropriately display/communicate and critically evaluate the solution procedure and the obtained results,
• develop exactness, consistency and diligence in communication, thinking and work,
• demonstrate an appropriate attitude towards engineering practice and science.

## Reference nosilca

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.

## Study materials

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

2. P. Šemrl, Osnove višje matematike 1, DMFA-založništvo, 2009.

3. M. Akveld, R. Sperb, Analysis I, vdf Hochschulverlag, ETH Zürich, 2009.

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