# Mathematics II

Higher education teachers: Dolinar Gregor
Collaborators: Cafuta Kristijan, Perne Andrej, Praprotnik Selena, Stopar Nik
Credits: 9
Semester: summer
Subject code: 64105

## Subject description

Prerequisits:

• Enrolment into the programme. Completed exam Mathematics I.

Content (Syllabus outline):

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 and careful and exact mathematical reasoning.
• To become familiar with the software for symbolic computations (e.g., Mathematica).

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,
• choose an appropriate mathematical tool,
• solve some types of ordinary differential equations,
• use of the software for solving technical problems,
• analyse and mathematically interpret technical problems,
• connect different mathematical tools for solving technical problems,
• critically evaluate the solution.

Learning and teaching methods:

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

## Study materials

1. G. Tomšič, N. Mramor Kosta, B. Orel: Matematika II, Založba FE in FRI, 2005.
2. P. Oblak, Matematika, Založba FE in FRI, 2014.
3. E. Kreyszig: Advanced engineering mathematics, John Wiley & Sons, 2006.
4. G. B. Thomas: Thomas' Calculus, Pearson Education, 2005.
5. David C. Lay: Linear algebra and its applications, Pearson, Addison Wesley, 2011.
6. N. Mramor Kosta, B. Jurčič-Zlobec: Zbirka nalog iz Matematike II, Založba FE in FRI, 2005.
7. G. Dolinar: Rešene naloge iz Matematike II za VSŠ, Založba FE in FRI, 2005.
8. Spletna učilnica eFEhttps://e.fe.uni-lj.si

# Study in which the course is carried out

• 1 year - 1st cycle - Electrical Engineering