We continue with our discussion of analytic and geometric properties of multivariable functions. For the former, we focus on the optimization of multivariable functions by using (partial) derivatives. For the latter, we consider the construction and analysis of more general and exotic surfaces using functions of two variables.
We then introduce the definition of an integral for a function of two variables: the double integral. This new integral can be computed by evaluating two single-variable integrals. We end this unit with a discussion of a few applications of double integrals.