# Mathematics II

Higher education teachers: Hajdinjak Melita
Collaborators: Cafuta Kristijan, Perne Andrej, Praprotnik Selena, Stopar Nik
Credits: 7
Semester: summer
Subject code: 64605

## Subject description

Prerequisits:

• Enrolment in the first year of study and completed exam Mathematics I.

The exam Mathematics I can be replaced by exams that cover the following topics: 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, continuity, limit), derivative of a function (derivation rules, geometric interpretation, differential, applications), integral of a function (indefinite integral, definite integral, applications of definite integral).

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). Linear ODE of higher orders (with constant coefficients, Euler's equation).

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. The acquired knowledge is indispensable in the study of Electrical Engineering.

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,
• use an appropriate mathematical tool in applicative electrotechnics,
• solve some types of ordinary differential equations,
• analyse simple applicative electrotechnical problems,
• connect different mathematical tools for solving technical problems,
• evaluate the solution.

Learning and teaching methods:

1. Lectures, tutorials,
2. and homework assignments.
3. Collective analysis, interpretation, and solving of technical problems.