Funkcije več spremenljivk : primeri in protiprimeri
Puntar, Janez (Author), Slapar, Marko (Mentor) More about this mentor... This link opens in a new window, Starčič, Tadej (Co-mentor)

URLURL - Presentation file, Visit http://pefprints.pef.uni-lj.si/id/eprint/5133 This link opens in a new window

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
Work type:Bachelor thesis/paper (mb11)
Tipology:2.11 - Undergraduate Thesis
Organization:PEF - Faculty of Education
Publisher:[J. Puntar]
Number of pages:IV, 24 str.
COBISS.SI-ID:12044105 This link opens in a new window
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Secondary language

Title:Functions of several variables: examples and counterexamples
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.

Keywords:mathematics, matematika

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