Vector Calculus: An Introduction

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 $\mathit{x}\in D$ a unique value denoted by $f(\mathit{x})\text{.}$ We call $D$ the domain of $f\text{,}$ and $\mathbb{R}$ is its range. If $N>3$ there is no way to visualise the functions. In the following we discuss ways to visualise functions of two and three variables.