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master's thesis
Polinomi i njihove derivacije
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:949290
Bogner, Anton
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Bogner, A. (2023). Polinomi i njihove derivacije (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:949290

Bogner, Anton. "Polinomi i njihove derivacije." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:949290

Bogner, Anton. "Polinomi i njihove derivacije." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:949290

Bogner, A. (2023). 'Polinomi i njihove derivacije', Master's thesis, University of Zagreb, Faculty of Science, accessed 22 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:949290

Bogner A. Polinomi i njihove derivacije [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2024 November 22] Available at: https://urn.nsk.hr/urn:nbn:hr:217:949290

A. Bogner, "Polinomi i njihove derivacije", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:949290

Metadata
TitlePolinomi i njihove derivacije
Title (english)Polynomials and their derivatives
AuthorAnton Bogner
MentorSanja Varošanec (mentor)
MentorMea Bombardelli (sumentor)
Committee memberSanja Varošanec (predsjednik povjerenstva)
Committee memberTomislav Bokulić (član povjerenstva)
Committee memberMea Bombardelli (član povjerenstva)
Committee memberLjiljana Arambašić (član povjerenstva)
Committee memberDamir Pajić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2023-09-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
Abstract
U ovom radu govorimo o poznatom teoremu, Bernsteinovoj nejednakosti za polinome i njihove derivacije. Polazeći od definicije polinoma i nekih bitnih teorema za holomorfne funkcije dolazimo do Bernsteinove nejednakosti i niza njezinih varijacija. Nadalje, proučavamo Erdos-Laxov i Turanov teorem za polinome, u kojima se pojavljuju uvjeti na položaj nultočaka. Na kraju dokazujemo nekoliko teorema u kojima se, za razliku od prijašnjih, javlja minimum modula polinoma i njegove prve derivacije.
Abstract (english)
In this paper we talk about the famous theorem, Bernstein’s inequality for polynomials and their derivatives. Starting from the definition of polynomials and some essential theorems for anayltic functions we obtain Bernstein’s inequality and a number of its variations. Furthermore, we study Erdos-Lax’s and Turan’s theorem for polynomials, which include conditions at the position of zeros. In the final chapter, we prove theorems in which, unlike the previous ones, the minimum of the modulus of the polynomial and its first derivation occurs.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:949290
Study programmeTitle: Mathematics and Physics Education; specializations in: Mathematics and Physics Education
Course: Mathematics and Physics Education
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: sveučilišni magistar edukacije matematike i fizike (sveučilišni magistar edukacije matematike i fizike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-01-30 11:00:43