Applied mathematics

There are no prerequisites.

Students familiarize themselves with the theoretical and practical background of the selected practical problem They use a vertical connection of knowledge they have acquired during their studies (analysis, linear algebra, discrete mathematics, numerical methods, optimization, databases, programming, etc.) to prepare guidelines for solving the problem, propose the use of appropriate methods, and implement the solution within the group in the appropriate programming environment. They test the solution on examples, present the solution, evaluate it and propose possible its improvements and generalizations.

Sodobni učbeniki in priročniki s področja analize, linearne algebre, diskretnih struktur, numeričnih metod, optimizacije, podatkovnih baz, programiranja,…
Zapiski s predavanj, gradiva za vaje in ostalo gradivo se v spletni učilnici predmeta letno posodablja in sledi sodobnim trendom/
Modern textbooks and manuals on the subjects of analysis, linear algebra, discrete structures, numerical methods, optimization, databases, programming, etc.
Lecture notes, exercise materials, and other resources are updated regularly in the subject's online classroom which follow modern trends.

Students become proficient in the combined use of different knowledge and working in a group to solve a complex problem. They learn how to choose the appropriate problem-solving methods and present the solution in the proper form. They are able to critically assess the final results, identify weaknesses in the chosen method, and propose some improvements.

The developed solution of the given problem in the chosen programming environment using the knowledge acquired during the previous learning process.
A properly prepared report on the problem-solving and on the obtained results.
A critical assessment of the developed solution, proposing improvements and generalizations.
Distinguishing between different methods of presenting the results.

Lectures, exercises, individual laboratory work, and group work, various forms of remote work, demonstration of results, and writing a final report.

preparation of the project
presentation
report preparation with the oral defence
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Jan Grošelj:
J. Grošelj, M. Knez, Generalized C1 Clough–Tocher splines for CAGD and FEM, Computer Methods in Applied Mechanics and Engineering 395 (2022), 114983, 22 str. [COBISS-SI-ID 125760515]
M. Kuralt, A. Cmok Kučič, R. Gašperšič, J. Grošelj, M. Knez, A. Filder, Gingival shape analysis using surface curvature estimation of the intraoral scans, BMC Oral Health 22, 283 (2022), 11 str. [COBISS-SI-ID 116774659]
J. Grošelj, M. Kapl, M. Knez, T. Takacs, V. Vitrih, A super-smooth C1 spline space over planar mixed triangle and quadrilateral meshes, Computers & Mathematics with Applications 80 (12) (2020), 2623–2643 [COBISS-SI-ID 34427395]
Matija Lokar:
A. Poberžnik, G. Bezjak, L. Jerše, S. Brezovnik, A. Arh-Klančar, N. Stopar, D. Smej Skutnik, F. Zupančič, J. Bajc, M. Lokar, V. Manfreda Kolar, Š. Rožanc, R. Krajnc, R. Repnik, P. Čeh, A. Žakelj, A. Triller, M. Cotič, E. Klemenčič, M. Ploj Vitrič in drugi, Razvijanje zmožnosti reševanja avtentičnih problemov z digitalnimi tehnologijami. Spletna izd. Ljubljana: Zavod RS za šolstvo, 2022. [COBISS-SI-ID 103284739]
G. Jerše in M. Lokar, Learning and teaching programming and numerical methods with a system for automatic assessment, 6th Central and Eastern European Conference on Computer Algebra and Dynamic Geometry Systems in Mathematics Education, 2016, Târgu Mureş, Romania, Cluj-Napoca: Sapientia - Hungarian University of Transylvania, 1-18. [COBISS-SI-ID 17830489]
M. Lokar, P. Libbrecht, Obstacles in combining the use of various tools in solving mathematical problems - why is Copy/Paste often useless, 6th Central and Eastern European Conference on Computer Algebra and Dynamic Geometry Systems in Mathematics Education, 2016, Târgu Mureş, Romania. Cluj-Napoca: Sapientia - Hungarian University of Transylvania, 1-15. [COBISS-SI-ID 17829977]
M. Lokar in M. Pretnar, A low overhead automated service for teaching programming. 15th Koli Calling Conference on Computing Education Research, 2015, Koli, Finland, 132-136. [COBISS-SI-ID 17536089]
Emil Žagar:
E. Žagar, Arc length preserving G2 Hermite interpolation of circular arcs, J. Comput. Appl. Math., 423 (2023), 115008, 12 str. [COBISS-SI-ID 134609923]
A. Vavpetič in E. Žagar, Geometric approximation of the sphere by triangular polynomial spline patches, Comput. Aided Geom. Design 92 (2022), 102061, 12 str. [COBISS-SI-ID 88497155],
R. T. Farouki, M. Knez, V. Vitrih in E. Žagar, On the construction of polynomial minimal surfaces with Pythagorean normals, Appl. Math. Comput. 435 (2022), 127439, 12 str. [COBISS-SI-ID 119810563]