# Mathematics I

Higher education teachers: Dolinar Gregor

Higher education teachers: , Šemrl Peter
Collaborators: Cafuta Kristijan, Perne Andrej, Praprotnik Selena, Stopar Nik
Credits: 9
Semester: winter
Subject code: 64101

## Subject description

Prerequisits:

• Enrolment in the first year of study.

Content (Syllabus outline):

Number systems (positive integers, rational numbers, real numbers, complex numbers). Sequences (accumulation points, 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).

Objectives and competences:

• To master the basic concepts of mathematical analysis and to be able to better understand them.
• To develop analytical thinking and careful and exact mathematical reasoning.

Intended learning outcomes:

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

• solve basic problems of mathematical analysis, including sequences, series, real functions, derivatives and integrals,
• choose an appropriate mathematical tool,
• compute the derivatives of elementary functions and integrals of some classes of functions,
• analyse and mathematically interpret technical problems,
• connect different mathematical tools for solving technical problems,
• critically evaluate the solution.

Learning and teaching methods:

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

## Study materials

1. G. Dolinar, Matematika 1, Založba FE in FRI, 2010.
2. P. Šemrl, Osnove višje matematike 1, DMFA-založništvo, 2009.
3. M. Akveld, R. Sperb, Analysis I, vdf Hochschulverlag, ETH Zürich, 2009.
4. G. B. Thomas: Thomas' Calculus, Pearson Education, 2005.
5. B. Jurčič-Zlobec, N. Mramor Kosta: Zbirka nalog iz Matematike I, Založba FE in FRI, 2009.
6. G. Dolinar, U. Demšar: Rešene naloge iz Matematike I za VSP, Založba FE in FRI, 2004.
7. Spletna učilnica eFE https://e.fe.uni-lj.si

# Study in which the course is carried out

• 1 year - 1st cycle - Electrical Engineering