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master's thesis
Primjena teorema o reziduumima na neprave integrale
Zagreb: University of Zagreb, Faculty of Science, 2020. urn:nbn:hr:217:028986
Radovčić, Marta
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Radovčić, M. (2020). Primjena teorema o reziduumima na neprave integrale (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:028986

Radovčić, Marta. "Primjena teorema o reziduumima na neprave integrale." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:028986

Radovčić, Marta. "Primjena teorema o reziduumima na neprave integrale." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:028986

Radovčić, M. (2020). 'Primjena teorema o reziduumima na neprave integrale', Master's thesis, University of Zagreb, Faculty of Science, accessed 29 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:028986

Radovčić M. Primjena teorema o reziduumima na neprave integrale [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2020 [cited 2024 December 29] Available at: https://urn.nsk.hr/urn:nbn:hr:217:028986

M. Radovčić, "Primjena teorema o reziduumima na neprave integrale", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:217:028986

Metadata
TitlePrimjena teorema o reziduumima na neprave integrale
Title (english)Application of residual theorems to false integrals
AuthorMarta Radovčić
MentorAna Prlić (mentor)
Committee memberAna Prlić (predsjednik povjerenstva)
Committee memberLjiljana Arambašić (član povjerenstva)
Committee memberMatija Kazalicki (član povjerenstva)
Committee memberJosip Tambača (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2020-09-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu proučavali smo primjenu teorema o reziduumima na različite tipove nepravih integrala. Rad je podijeljen na tri poglavlja. U prvom poglavlju navedeni su osnovni pojmovi te iskazani teoremi povezani s teorijom reziduuma koji se koriste u radu. U drugom poglavlju promatrali smo primjenu teorema o reziduumima na neprave integrale. Pritom smo kao podintegralne funkcije promatrali racionalne funkcije te funkcije oblika: \( f(x) \cos px, \ f(x) \sin px , \ \frac{f(x)}{x^{\alpha}}, \ f(x) \ln x, \) gdje je \( f(x) \) racionalna funkcija. Za svaki od navedenih tipova dan je detaljan izvod formule prema kojoj se računaju nepravi integrali. U sklopu tog poglavlja promatrali smo kako se računa Fourierov transformat racionalne funkcije. U posljednjem poglavlju proučavali smo kompleksnu gama funkciju, područje na kojem je definirana, glavna svojstva te njezinu primjenu u integralnom računu.
Abstract (english)
In this thesis we studied the applications of the residue theorem on various types of improper integrals. The thesis is divided into three chapters. In the opening chapter we defined the basic concepts and we stated theorems related to the residue theory used in this thesis. In the second chapter we studied the applications of the residue theorem to improper integrals. We studied integrals of rational functions and functions like: \( f(x) \cos px, \ f(x) \sin px , \ \frac{f(x)}{x^{\alpha}}, \ f(x) \ln x, \) where \( f(x) \) is a rational function. For each of these types we gave formulas for calculating improper integrals. Also, in this chapter we studied a Fourier transform of a rational function. In the last chapter, we studied the complex Gamma function, its domain, the main properties and applications in integral calculus.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:028986
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-03-11 13:12:22