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Leibniz-Newtonova formula in njene posplošitve : diplomsko deloTopler, SaraV diplomskem delu obravnavamo Leibniz-Newtonovo formulo in njene posplošitve. Pojem Riemannovega oz. določenega integrala je vpeljan s pomočjo Darbouxovih in Riemannovih vsot, pri čemer je poudarjena ... ekvivalentnost omenjenih pristopov. V tretjem poglavju so predstavljeni potrebni pogoji za integrabilnost funkcij, v četrtem pa ena izmed povezav med določenimi integrali in primitivnimi funkcijami. Sledi pomemben matematični rezultat Leibniza in Newtona, t. i. Leibniz-Newtonova formula, znana tudi kot osnovni izrek analize. V nadaljevanju obravnavamo posplošitve te formule; pri prvi obliki nadomestimo obojestranski odvod z desnim odvodom, v drugi nastopa Schwarzov odvod, tretja posplošitev Leibniz-Newtonove formule pa se nanaša na funkcije, ki izpolnjujejo Lipschitzev pogoj. V zadnjem poglavju je navedenih nekaj primerov, kjer postane računanje določenega integrala s pomočjo Leibniz-Newtonove formule precej lažje kot računanje po definiciji določenega integrala. Ključna sta primera, ki ponazarjata napake, ki nastanejo pri uporabi rešitev iz tablic nedoločenih integralov na neustreznih intervalih. Pokazali smo, kako se tem napakam uspešno izogniti.Type of material - undergraduate thesis ; adult, seriousPublication and manufacture - Maribor : [S. Topler], 2012Language - slovenianCOBISS.SI-ID - 19087368
Author
Topler, Sara
Other authors
Milutinović, Uroš
Topics
Leibniz, Gottfried Wilhelm, 1646-1716 |
Newton, Isaac, 1643-1727 |
Univerzitetna in visokošolska dela |
matematika |
vsote |
integrali |
določeni integrali |
primitivna funkcija |
desni odvod |
formule |
diplomska dela
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Library | Call number – location, accession no. ... | Copy status |
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Miklošič Library FPNM, Maribor | M DIPL 51 TOPLER S. Leibniz IN: 920120020 |
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Topler, Sara | ![]() |
Milutinović, Uroš | 08727 |
Source: Personal bibliographies
and: SICRIS
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