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.