We begin with an introduction to functions of several variables, their use, and their methods of visualization. These functions can be used to model real-world quantities and describe many different curves and surfaces.
In order to study these features, we borrow the idea of derivatives from single-variable calculus and apply it to the multivariable setting. This, in turn, will allow us to study both the analytic (e.g. approximations) and geometric (e.g. tangent planes) properties of multivariable functions.