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Functions of several variables: examples and counterexamples

Janez Puntar (2018) Functions of several variables: examples and counterexamples. Diploma thesis.

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    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.

    Item Type: Thesis (Diploma thesis)
    Keywords: functions of several variables, partial derivatives, Schwarz's theorem, differentiability
    Number of Pages: 24
    Language of Content: Slovenian
    Mentor / Comentors:
    Mentor / ComentorsIDFunction
    izr. prof. dr. Marko SlaparMentor
    asist. dr. Tadej StarčičComentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=50126&select=(ID=12044105)
    Institution: University of Ljubljana
    Department: Faculty of Education
    Item ID: 5133
    Date Deposited: 10 Jul 2018 12:10
    Last Modified: 10 Jul 2018 12:10
    URI: http://pefprints.pef.uni-lj.si/id/eprint/5133

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