# Mathematics III

## Subject description

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 competences

To upgrade the basic concepts of mathematical analysis, procedures, and laws. Further develop analytical thinking, careful and exact mathematical reasoning as well as other building blocks of science/mathematics/engineering literacy. To upgrade the knowledge of the software for symbolic computations (e.g., Mathematica).

## Teaching and learning methods

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

## Expected study results

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,
• compute basic multiple, line and surface integrals,
• identify and understand problems in differently structured environments/contexts, carry out independent research,
• identify, analyse and use mathematical and ICT tools to solve natural science and engineering authentic problems,
• appropriately display/communicate and critically evaluate the solution procedure and the obtained results,
• master exactness, consistency and diligence in communication, thinking and work,
• demonstrate an appropriate attitude towards engineering practice and science.

## Basic sources and literature

1. M. Hajdinjak, G. Dolinar: Matematika III, zapiski predavanj, https://e.fe.uni-lj.si, 2021.
2. G. Tomšič, T. Slivnik: Matematika III,  Založba FE, Ljubljana, 2001.
3. R. Sperb, Analysis II, vdf Hochschulverlag, ETH Zürich, 2011.
4. E. Kreyszig: Advanced engineering mathematics, John Wiley & Sons, 2006
5. G. B. Thomas: Thomas' Calculus, Pearson Education, 2005
6. T. Žitko: Zbirka nalog iz Matematike III, Založba FE, 2002.
7. G. Dolinar: Rešene naloge iz Matematike III, Založba FE in FRI, Ljubljana, 2005.
8. Spletna učilnica eFE https://e.fe.uni-lj.si

## Stay up to date

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