# Mathematics IV

## Subject 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).

## Teaching and learning methods

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

## Expected study results

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.

## Basic sources and literature

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

## Stay up to date

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