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undergraduate thesis
Elementarne nejednakosti
Split: University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, 2022. urn:nbn:hr:179:492487
Kardum, Mirta
University of Split
Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture
Department of Mathematics and Physics

Institutional repository: Repository of the Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture

Cite this document

Kardum, M. (2022). Elementarne nejednakosti (Undergraduate thesis). Split: University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture. Retrieved from https://urn.nsk.hr/urn:nbn:hr:179:492487

Kardum, Mirta. "Elementarne nejednakosti." Undergraduate thesis, University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, 2022. https://urn.nsk.hr/urn:nbn:hr:179:492487

Kardum, Mirta. "Elementarne nejednakosti." Undergraduate thesis, University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, 2022. https://urn.nsk.hr/urn:nbn:hr:179:492487

Kardum, M. (2022). 'Elementarne nejednakosti', Undergraduate thesis, University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, accessed 01 December 2024, https://urn.nsk.hr/urn:nbn:hr:179:492487

Kardum M. Elementarne nejednakosti [Undergraduate thesis]. Split: University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture; 2022 [cited 2024 December 01] Available at: https://urn.nsk.hr/urn:nbn:hr:179:492487

M. Kardum, "Elementarne nejednakosti", Undergraduate thesis, University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Split, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:179:492487

Metadata
TitleElementarne nejednakosti
Title (english)Elementary inequalities
AuthorMirta Kardum
MentorJosipa Barić (mentor)
GranterUniversity of Split
Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture
(Department of Mathematics and Physics)
Split
Defense date and country2022-09-21, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Computing
Abstract
Nejednakost je pojam o nejednakoj usporedbi dvaju brojeva ili matematičkih izraza. One su važan dio matematike koji uvelike doprinosi proširenju našeg znanja potrebnog za suočavanje s kompleksnijim problemima i zadacima, ali i za primjenu u znanosti. Kako bi bolje razumjeli samu svrhu nejednakosti, kako se one rješavaju i primjenjuju, potrebno je dobro se upoznati s elementarnim nejednakostima i njihovim svojstvima. U ovom radu detaljno su prikazane, ilustrirane i dokazane neke od najpoznatijih elementarnih nejednakosti: nejednakost između aritmetičke i geometrijske sredine, težinska nejednakost između aritmetičke i geometrijske sredine, Bernoullijeva, Cauchy-Schwarzova, Čebiševljeva, Hölderova i nejednakost Minkowskog. Pokazane su i povezanosti među navedenim nejednakostima gdje se nerijetko jedna nejednakost može izvesti iz druge i obratno, pa tako iz ovih nejednakosti dobivamo korisne nejednakosti za eksponencijalnu i logaritamsku funkciju koje su također obrađene u ovom radu.
Abstract (english)
Inequality is the concept of an unequal comparison of two numbers or mathematical expressions. They are an important part of mathematics that greatly contributes to the expansion of our knowledge needed to deal with more complex problems and tasks, but also for application in science. In order to better understand the very purpose of inequalities, how they are solved and applied, it is necessary to become familiar with elementary inequalities and their properties. In this paper, some of the most well-known elementary inequalities are presented, illustrated and proved in detail: the inequality between the arithmetic and geometric mean, the weighted inequality between the arithmetic and geometric mean, Bernoulli’s, Cauchy-Schwarz’s, Chebyshev’s, Hölder’s and Minkowski’s inequality. Connections between the mentioned inequalities are also shown, where often one inequality can be derived from another and vice versa, so from these inequalities we get useful inequalities for exponential and logarithmic functions, which are also discussed in this paper.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:179:492487
Study programmeTitle: Computing
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
Type of resourceText
File originBorn digital
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Created on2023-05-19 11:48:55