Konstrukcija nikjer odvedljive zvezne funkcije

diplomsko delo

Gloria Vidmar (Author), Marko Slapar (Mentor)

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.

Keywords

realna funkcija;Weierstrassova funkcija;van der Waerden-Takagijeva funkcija;

Data

Language:	Slovenian
Year of publishing:	2015
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[G. Vidmar]
UDC:	517.51(043.2)
COBISS:	10686281
Views:	740
Downloads:	157
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	The construction of nowhere differentiable continuous function
Secondary 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.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Bachelor thesis/paper
Thesis comment:	Univ. Ljubljana, Pedagoška fak., Dvopredmetni učitelj
Pages:	23 str.
ID:	8900809