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undergraduate thesis
Neelementarni integrali
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. urn:nbn:hr:126:197381
Vuković, Ivan
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

Institutional repository: Repository of School of Applied Mathematics and Informatics

Cite this document

Vuković, I. (2022). Neelementarni integrali (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:197381

Vuković, Ivan. "Neelementarni integrali." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:197381

Vuković, Ivan. "Neelementarni integrali." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:197381

Vuković, I. (2022). 'Neelementarni integrali', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 30 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:197381

Vuković I. Neelementarni integrali [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2022 [cited 2024 November 30] Available at: https://urn.nsk.hr/urn:nbn:hr:126:197381

I. Vuković, "Neelementarni integrali", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:126:197381

Metadata
TitleNeelementarni integrali
Title (english)Nonelementary Integrals
AuthorIvan Vuković
MentorIvan Soldo (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2022-09-19, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Mathematical Analysis
Abstract
U ovom radu proučavat ćemo elementarna polja i elementarne funkcije te vidjeti kako se njihova teorija može primijeniti na neelementarne integrale, tj. integrale funkcija čije primitivne funkcije nisu elementarne. Dat ćemo nekoliko primjera takvih integrala i njihovu primjenu. Posebno ćemo se baviti Gaussovim integralom: dokazat ćemo da je konvergentan, da integral \(\int e^{-x^{2}}dx\) nije elementaran te ćemo ga riješiti na tri različita načina koristeći različita područja matematike. Na samom kraju koristit ćemo numeričku integraciju kako bismo ga aproksimirali.
Abstract (english)
In this paper we will study elementary fields and elementary functions and see how that theory can be applied to nonelementary integrals, that is integrals of functions whose primitive functions are not elementary. We will give a few examples of such integrals and see where they can be applied. We will focus on the Gaussian integral: prove its convergence, prove that integral \(\int e^{-x^{2}}dx\) is nonelementary and solve it in three different ways using several branches of mathematics. Finally, we will apply the numerical method to approximately calculate its value.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:197381
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-09-20 07:25:00