Matematika I

Higher education teachers: Dolinar Gregor
Collaborators: Cafuta Kristijan, Perne Andrej, Stopar Nik, Žitko Tomislav

Subject description

Prerequisits:

• Enrolment into the programme

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:

• Knowledge and understanding of the basic concepts of mathematical analysis, including sequences, series, real functions, derivatives, integrals.
• The ability to analyse and mathematically interpret technical problems.

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. G. Tomšič, B. Orel, N. Mramor Kosta: Matematika I, Založba FE in FRI, Ljubljana, 2004
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, Ljubljana, 2009
6. G. Dolinar, U. Demšar: Rešene naloge iz Matematike I za VSP, Založba FE in FRI, Ljubljana, 2004
7. Spletna stran http://matematika.fe.uni-lj.si/