In this section we extend some concepts that we introduced in the previous concerning calculus for functions of one variable. What we really need for what follows is to get an intuitive idea of how some basic concepts are generalized when we consider a function of multiple variables, i.e., a function f(x1, x2, …, xn) = f(x) mapping a vector in 
to a real number. In particular, we would like to see
- How we can extend the concept of derivative
- How we can extend the Taylor’s expansion
- What is an integral in multiple dimensions
The first two issues are relevant from an optimization perspective, and they are strictly linked to linear algebra. Multiple integrals play a more limited role in the book, as they will be used only to deal with probability distributions of multiple random variables.
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