# Mathematics III

Higher education teachers: Dolinar Gregor

Higher education teachers: , Hajdinjak Melita
Collaborators: Cafuta Kristijan, Perne Andrej, Stopar Nik
Credits: 9
Semester: winter
Subject code: 64111

## Subject description

Prerequisits:

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

Content (Syllabus outline):

Differential geometry (curves, surfaces in three-dimensional Euclidean space). Multiple integral (parameter-dependent integral, double and triple integral). Vector analysis (gradient, divergence, curl, nabla operator). Line and surface integrals (Green’s theorem, divergence theorem of Gauss, Stokes’s theorem). Complex analysis (complex analytic functions, elementary complex functions, complex integration, Laurent series, theory of residues).

Objectives and competencies:

• 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:

• solve basic problems of differential geometry and mathematical analysis, including vector and complex analysis,
• choose an appropriate mathematical tool,
• compute basic multiple, line and surface integrals,
• use appropriate mathematical 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. 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

• 2 year - 1st cycle - Electrical Engineering