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Konstrukcija nikjer odvedljive zvezne funkcije : diplomsko delo
ID Vidmar, Gloria (Author), ID Slapar, Marko (Mentor) More about this mentor... This link opens in a new window

URLURL - Presentation file, Visit http://pefprints.pef.uni-lj.si/3005/ This link opens in a new window

Abstract
V prvem delu diplomskega dela najprej ponovimo nekaj lastnosti realne funkcije, zveznosti, odvedljivosti in funkcijskih vrst, saj so ti pojmi ključni za razumevanje nikjer odvedljivih funkcij. V drugem delu je predstavljenih nekaj novih izrekov in pojmov, kot je na primer Labesguov izrek in funkcije z omejeno variacijo ter Weierstrassova funkcija, ki velja za prvi primer nikjer odvedljive funkcije. V zadnjem delu diplomskega dela je predstavljena van der Waerden-Takagijeva funkcija z generaliziranimi parametri in dokaz, da je funkcija zvezna in nikjer odvedljiva.

Language:Slovenian
Keywords:realna funkcija, Weierstrassova funkcija, van der Waerden-Takagijeva funkcija
Work type:Bachelor thesis/paper
Typology:2.11 - Undergraduate Thesis
Organization:PEF - Faculty of Education
Publisher:[G. Vidmar]
Year:2015
Number of pages:23 str.
PID:20.500.12556/RUL-72397 This link opens in a new window
UDC:517.51(043.2)
COBISS.SI-ID:10686281 This link opens in a new window
Publication date in RUL:16.09.2015
Views:1413
Downloads:274
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Secondary language

Language:English
Title:The construction of nowhere differentiable continuous function
Abstract:
In first part of this thesis some basic concepts are repeated, such as continuity, differentiability and functional series since we must understands those concepts to understand nowhere differentiable functions. In the second part we present some new theorems and concepts, such as Labesgue theorem, functions with bounded variation and Weierstrass function, which is the first example of nowhere differentiable continuous function. In the last part of thesis the van der Waerden-Takagi function with generalized parameters is presented, also with proof that this funciton is nowhere differentiable but continuous everywhere.

Keywords:functions

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