In this chapter we begin the analysis of functions of more than one variable. These functions do not, as in the case of one variable, have a domain in #\mathbb R#, but rather in #{\mathbb R}^n#, where #n# is a natural number that is greater than #1#. It is #{\mathbb R}^n# the set of #n#-tuples of real numbers. This collection is a vector space (a concept from the course Linear Algebra), but that fact, we will make little use.

Many concepts such as continuity, limits, and differentiation, and results like criteria in terms of derivatives for the existence of local extrema, are versions for more variables that match with what is already known for the case of one variable.

We focus primarily on partial derivatives and their significance for finding extreme values ​​of functions of two variables.