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master's thesis
Neke generalizacije Lagrangeovog teorema srednje vrijednosti
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:643387
Matika, Monika
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Matika, M. (2015). Neke generalizacije Lagrangeovog teorema srednje vrijednosti (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:643387

Matika, Monika. "Neke generalizacije Lagrangeovog teorema srednje vrijednosti." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:643387

Matika, Monika. "Neke generalizacije Lagrangeovog teorema srednje vrijednosti." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:643387

Matika, M. (2015). 'Neke generalizacije Lagrangeovog teorema srednje vrijednosti', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:643387

Matika M. Neke generalizacije Lagrangeovog teorema srednje vrijednosti [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:643387

M. Matika, "Neke generalizacije Lagrangeovog teorema srednje vrijednosti", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:643387

Metadata
TitleNeke generalizacije Lagrangeovog teorema srednje vrijednosti
AuthorMonika Matika
MentorLjiljana Arambašić (mentor)
Committee memberLjiljana Arambašić (predsjednik povjerenstva)
Committee memberDamir Bakić (član povjerenstva)
Committee memberBoris Guljaš (član povjerenstva)
Committee memberMiljenko Marušić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-02-26, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu smo proučavali teoreme srednje vrijednosti te njihove generalizacije. Prvo smo proučili Lagrangeov, Rolleov, Cauchyjev te Flettov teorem srednje vrijednosti za realne funkcije realne varijable te prikazali njihove geometrijske interpretacije. Osim toga, na primjerima smo ilustrirali kako navedene teoreme koristiti prilikom rješavanja zadataka. Nakon toga, promatrali smo teoreme srednje vrijednosti i njihove generalizacije za funkcije više varijabli i to prvo za realne funkcije više varijabli, zatim za vektorske funkcije jedne realne varijable te na kraju za vektorske funkcije više realnih varijabli. Na primjeru smo pokazali kako se teorem srednje vrijednosti ne može na direktan način proširiti na vektorske funkcije. Za kraj smo diskutirali teoreme srednje vrijednosti za kompleksne funkcije kompleksne varijable.
Abstract (english)
In this paper we studied the mean value theorems and theirs generalizations. First we considered Lagrange’s, Rolle’s, Cauchy’s and Flett’s mean value theorem for real-valued functions of a real variable and showed their geometric interpretations. Furthermore, we gave examples to illustrate how we can use these theorems in solving problems. After that, we considered the mean value theorems and theirs generalizations for the functions of several variables, first for the real-valued functions of several real variables, then for the vector valued functions of one real variable and, finally, for the vector-valued functions of several real variables. In addition, we gave an example to illustrate that the mean value theorem cannot be directly extended in this more general situation. Finally, we discussed the mean value theorem for the complex-valued functions of a complex variable.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:643387
Study programmeTitle: Mathematical Statistics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to students and staff of home institution
Terms of useLicence In copyright icon
Created on2019-01-23 11:37:31