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Verižni ulomki in vrste : diplomsko deloFerk, Sonja, 1987-V tem diplomskem delu preučujemo zvezo med navadnimi verižnimi ulomki in neskončnimi številskimi vrstami. V prvem poglavju opišemo osnove teorije navadnih verižnih ulomkov. Posebej obravnavamo ... končne, neskončne in periodične verižne ulomke. Verižni ulomki so uporabni pri iskanju najboljših racionalnih aproksimacij iracionalnih števil. Mnogi matematiki so se v preteklosti ukvarjali s problemom, kako povezati verižne ulomke z vrstami. V drugem poglavju izpeljemo pomembne rezultate, ki povezujejo navadne verižne ulomke in vrste. Prvi pomembni rezultat je izrek, s katerim kvadratično iracionalno število razvijemo v vrsto, katere delne vsote so konvergenti ustreznega navadnega verižnega ulomka. Obratno lahko ta izrek uporabimo za iskanje navadnih verižnih ulomkov vsot nekaterih tipov vrst. V zadnjem poglavju obravnavamo Newtonovo metodo, s katero dobimo zaporedne približke kvadratično iracionalnih števil in jih primerjamo s približki kvadratično iracionalnih števil pridobljenimi s konvergenti navadnega verižnega ulomka.Type of material - undergraduate thesis ; adult, seriousPublication and manufacture - Maribor : [S. Ferk], 2012Language - slovenianCOBISS.SI-ID - 19472648
Author
Ferk, Sonja, 1987-
Other authors
Eremita, Daniel
Topics
Univerzitetna in visokošolska dela |
verižni ulomki |
zaporedja |
periodični verižni ulomki |
končni verižni ulomki |
neskončni verižni ulomki |
Newtonova metoda |
diplomska dela
Library | Call number – location, accession no. ... | Copy status |
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Miklošič Library FPNM, Maribor | M DIPL 51 FERK S. Verižni IN: 920120103 |
available - reading room |
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Ferk, Sonja, 1987- | |
Eremita, Daniel | 19550 |
Source: Personal bibliographies
and: SICRIS
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