Funkcije več spremenljivk

primeri in protiprimeri

Janez Puntar (Author), Marko Slapar (Mentor), Tadej Starčič (Co-mentor)

Abstract

V diplomskem delu obravnavamo osnovne lastnosti funkcij več spremenljivk. Osredotočimo se na zveznost, parcialno odvedljivost, Schwarzov izrek in diferenciabilnost funkcij. Na primerih bomo ilustrirali, da zveznost in parcialna odvedljivost nista zgolj preprosti posplošitvi analognih pojmov pri funkcijah ene spremenljivke in s primeri ilustrirali Schwarzov izrek. Pokazali bomo, da je zveznost parcialnih odvodov zadosten pogoj za diferenciabilnost, ni pa potreben.

Keywords

funkcije več spremenljivk;parcialni odvodi;Schwarzov izrek;diferenciabilnost;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[J. Puntar]
UDC:	51(043.2)
COBISS:	12044105
Views:	1637
Downloads:	306
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Functions of several variables: examples and counterexamples
Secondary abstract:	In the Diploma thesis we discuss the basic properties of functions of several variables. We focus on continuity, partial derivatives, Schwarz's theorem and differentiablaty. We present examples that illustrate that continuity and partial differentiation are not merely simple generalizations of analogous terms in the theory of functions of one variable. We also use examples to illustrate Schwarz's theorem. We show that continuity of partial derivatives is a sufficient but not necessary condition for differentiability.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Bachelor thesis/paper
Thesis comment:	Univ. v Ljubljani, Pedagoška fak., Dvopredmetni učitelj, Matematika-računalništvo
Pages:	IV, 24 str.
ID:	10944832