Understanding the difficulties in applying some mathematical concepts to the study of physics

Ukratko, diplomski rad je napisan s ciljem istražiti razumjevanje u primjeni matematičkih koncepata kod studenata Fizičkog odsijeka Prirodoslovno-matematičkog fakulteta u Zagrebu. Matematički koncpeti koje smo provjeravali su integrali i gradijenti. Istraživanje se sastojalo od nekoliko koraka. Prvo smo u razgovoru sa starijim studentima istražili koji su im matematički koncepti zadavali najviše problema tijekom fakultetskog obrazovanja. Nakon toga smo dali pitanja otvorenog tipa ne bi li se skupilo sto više smjerova razmišljanja i ponudilo kasnije u testu zatvorenog tipa kao odgovore što smo onda proveli na većem uzorku ispitanika. Istraživanje smo proveli pomoću konceptualnog testa u online formatu na platformi Microsoft Forms. Kod integrala ispitali smo pretvaranje fizikalnog problema u matematički izraz, fizikalnu interpretaciju pojedinih matematičkih simbola i izraza te mjerne jedinice fizikalnih veličina. U dijelu ispitivanja razumijevanja gradijenta provjerili smo znaju li studenti računski pronaći vektor gradijenta u određenoj točki funkcije, ponudili smo im neke zadatke iz elektrodinamike u kojima smo htjeli provjeriti njihovu primjenu te na kraju i grafičko određivanje vektora gradijenta u danoj točki. U jednom od koraka istraživanja provjerili smo i proporcionalnost i omjere koji su ostali kao uvod za daljnja proučavanja i ispitivanja. Na kraju diplomskog rada predložili smo način uklanjanja uočenih poteškoća.The graduate thesis was written with the intention of investigating the understanding of the application of mathematical concepts with the students of the Physics department at the Faculty of Science at the University of Zagreb. The mathematical concepts which were inspected were integrals and gradients. The research consisted of a few steps. Firstly, through a conversation with the older students at the university, we tried to find out which mathematical concepts gave them the most trouble throughout their education at the university. Afterwards, we gave out open-type questions so we could collect as many opinions from students from different departments, and later on, offered closed-type questions, which we carried out across a larger number of respondents. The research was carried out through a conceptual exam in an online form through the platform of Microsoft Forms. When it came to integrals, we examined the conversion of problems in physics into mathematical expressions, the physical interpretation of individual mathematical symbols and expressions, and then the metric units of physical quantities. In the part of the research where we examined the understanding of the gradient, we inspected if the students knew how to numerically find the vector of the gradient at a given point. In one of the steps of the research, we inspected the proportions and the rations which remained as an introduction to further studies and research. At the end of the thesis, we suggested a way to eliminate the said difficulties