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undergraduate thesis
Osnovni teoremi diferencijalnog i integralnog računa
2018. urn:nbn:hr:126:467356
Mihalj, Glorija
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Algebra, Analysis and Number Theory Research Group

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Mihalj, G. (2018). Osnovni teoremi diferencijalnog i integralnog računa (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:467356

Mihalj, Glorija. "Osnovni teoremi diferencijalnog i integralnog računa." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:467356

Mihalj, Glorija. "Osnovni teoremi diferencijalnog i integralnog računa." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:467356

Mihalj, G. (2018). 'Osnovni teoremi diferencijalnog i integralnog računa', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 04 February 2025, https://urn.nsk.hr/urn:nbn:hr:126:467356

Mihalj G. Osnovni teoremi diferencijalnog i integralnog računa [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2018 [cited 2025 February 04] Available at: https://urn.nsk.hr/urn:nbn:hr:126:467356

G. Mihalj, "Osnovni teoremi diferencijalnog i integralnog računa", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:126:467356

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Metadata
TitleOsnovni teoremi diferencijalnog i integralnog računa
Title (english)Fundamental Theorems of Calculus
AuthorGlorija Mihalj
MentorIvan Soldo (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Algebra, Analysis and Number Theory Research Group)
Osijek
Defense date and country2018-09-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Mathematical Analysis
Abstract
U ovom radu proučavat ćemo osnovne teoreme diferencijalnog i integralnog računa. Diferencijalni račun obilježili su teoremi o srednjim vrijednostima (Rolleov, Lagrangeov i Cauchyjev) koje ćemo iskazati i dokazati te objasniti njihovo geometrijsko značenje. Također ćemo iskazati i dokazati Fermatov teorem koji je poznat kao nužan uvjet za postojanje ekstrema, ali i za dokazivanje Rolleovog teorema. Pod osnovne teoreme integralnog računa navest ćemo Riemannov teorem, teorem o monotonosti, teorem srednje vrijednosti za integral neprekidne funkcije te jednu od najznačajnijih formula - Newton-Leibnizovu formulu koja nam daje vezu izmedu odredenog i neodredenog integrala.
Abstract (english)
In this paper, we will consider fundamental theorems of calculus. The primary objects of study in differential calculus are The mean value theorems (Rolle’s, Lagrange’s and Cauchy’s) that we will prove and give their geometric interpretation. Also, we will make a statement and a proof of Fermat’s theorem known as a necessary condition in existance of local minimum and maximum. In Section 2, we will discuss Riemann’s theorem, the theorem on monotone functions, the mean value theorem for integrals and one of the most important formula - Newton-Leibniz formula that gives us the connection between the indefinite and the definite integral.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:467356
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
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Created on2018-10-17 06:35:48