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Chapter 2 Functions of Several Variables

Suppose that \(D\subset\mathbb R^N\text{.}\) We consider functions defined on \(D\) with values in \(\mathbb R\text{.}\) A function, \(f\text{,}\) as usual assigns to every \(\vect x\in D\) a unique value denoted by \(f(\vect x)\text{.}\) We call \(D\) the domain of \(f\text{,}\) and \(\mathbb R\) is its range. If \(N\gt 3\) there is no way to visualise the functions. In the following we discuss ways to visualise functions of two and three variables.