Mathematics II

Course description

Matrices (basic operations, matrix product, rank, determinant, eigenvalues, eigenvectors, linear transformations). Systems of linear equations (Gauss elimination, Cramer's rule).

Vectors (basic operations, scalar product, vector product, scalar triple product, analytic geometry). Function series (power series, Taylor series, Fourier series). Functions of two and more variables (partial derivatives, chain rule, extrema, conditional extrema). Ordinary differential equations (ODE) of the first order (with separable variables, linear, first integral). Linear ODE of higher orders (with constant coefficients, Euler's equation). Linear systems of ODEs, linearly independent solutions.

Objectives and competences

To present and upgrade basic mathematical concepts, procedures, and laws, and to deepen their understanding. To develop analytical thinking, careful and exact mathematical reasoning as well as other building blocks of science/mathematics/engineering literacy. To become familiar with 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 mathematical analysis and linear algebra, including matrices, vectors, function series, functions of several variables and ordinary differential equations,
• solve some types of ordinary differential equations,
• identify and understand problems in differently structured environments/contexts,
• 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,
• 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 II, zapiski predavanj, https://e.fe.uni-lj.si, 2021.

2. G. Tomšič, N. Mramor Kosta, B. Orel: Matematika II,  Založba FE in FRI, 2005.

3. P. Oblak, Matematika, Založba FE in FRI, 2014.

4. E. Kreyszig: Advanced engineering mathematics, John Wiley & Sons, 2006.

5. G. B. Thomas: Thomas' Calculus, Pearson Education, 2005.

6. David  C. Lay, Linear algebra and its applications, Pearson, Addison Wesley, 2011.

7. K. Cafuta, M. Hajdinjak, A. Perne: Zbirka nalog iz Matematike II, Založba FE, 2018.

8. N. Mramor Kosta, B. Jurčič-Zlobec: Zbirka nalog iz Matematike II, Založba FE in FRI, 2005.

9. G. Dolinar: Rešene naloge iz Matematike II za VSŠ, Založba FE in FRI, 2005.

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

Bodi na tekočem

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