**Note**: Before reading this node, it is highly recommendable to have some notion of

calculus. Please be familiar with calculus or the contents of that node before reading further.

Simply put, multivariable calculus is the study of calculus with more than one

independent variable.

Vector calculus depends heavily on multivariable calculus. Often times, when this subject is taught, only the two-variable case is dealt with, and "these

results

extend to as many variables as you may be working with" is a

common mantra.

Some highlights:

The notion of '

derivative' is replaced with '

directional derivative'.

Some

area and

length calculation

questions become easier. See

Green's Theorem for specific

function alterations.

Fluid mechanics becomes available as an area of study.

Concepts like

irrotational,

divergence and

gradient become important.

*Since I took my time about updating this w/u, another, admittedly better, one has appeared. I think my generalizations and the other's specifics are a good combination, so I won't try to re-do all the work already done.*