# Mathematics IV

Higher education teachers: Dolinar Gregor

Higher education teachers: , Hajdinjak Melita
Collaborators: Cafuta Kristijan, Perne Andrej
Credits: 6
Semester: summer
Subject code: 64115

## Subject description

Prerequisits:

• Enrollment in the second year of study. Completed exams Mathematics I, Mathematics II and Mathematics III.

Content (Syllabus outline):

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.
• To develop analytical thinking and careful and exact mathematical reasoning.
• To upgrade the knowledge of the software for symbolic computations (e.g., Mathematica).

Intended learning outcomes:

After successful completion of the course, students should be able to:

• knowledge of integral transformations, some special functions, and calculus of variations,
• solve some of the most important partial differential equations,
• use of the software for solving technical problems,
• critically analyse of the use of the basic mathematical procedures and laws for solving technical problems that we encounter in practise,
• identify, analyse and connect different mathematical tools for solving technical problems,
• critically evaluate the solution,
• master exactness, consistency, diligence, and tidiness.

Learning and teaching methods:

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

## Study materials

1. G. Tomšič, T. Slivnik: Matematika IV, Založba FE in FRI, Ljubljana, 2004.
2. E. Kreyszig: Advanced engineering mathematics, John Wiley & Sons, 2006.
3. R. L. Burden, J. D. Faires: Numerical Analysis, 9th Edition, Brooks/Cole, 2011.
4. L. Komzsik: Applied Calculus of Variations for Engineers, CRC Press, Taylor & Francis Group, Boca Raton, 2009.
5. T. Žitko: Zbirka nalog iz Matematike IV, Založba FE in FRI, Ljubljana, 2004.
6. Spletna učilnica eFE https://e.fe.uni-lj.si

# Study in which the course is carried out

• 2 year - 1st cycle - Electrical Engineering