We now turn to the analysis of functions of several variables. We therefore consider functions \(f: D \to W\) with \(D \subseteq {\mathbb R}^n\) and \(W \subseteq {\mathbb R}^m\) for natural numbers m and n. To this end, we first show with numerous examples, what types of such functions can still be illustrated. Finally, we generalise open and closed intervals, sequences and limits of sequences to the vector space \({\mathbb R}^n\) and finally explain the continuity of functions of several variables analogous to the case of a function of one variable.

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Functions of Several Variables

  • Christian Karpfinger

摘要

We now turn to the analysis of functions of several variables. We therefore consider functions \(f: D \to W\) with \(D \subseteq {\mathbb R}^n\) and \(W \subseteq {\mathbb R}^m\) for natural numbers m and n. To this end, we first show with numerous examples, what types of such functions can still be illustrated. Finally, we generalise open and closed intervals, sequences and limits of sequences to the vector space \({\mathbb R}^n\) and finally explain the continuity of functions of several variables analogous to the case of a function of one variable.