Running Multivariable Resources
math testWe’ve hit the big three theorems of vector calculus: Green’s, Stokes’, and the Divergence
Theorem (although Green’s theorem is really a pretty obvious special case of Stokes’ theorem). But it’s an amazing fact that all of these theorems are really special cases of an even
larger theorem that unifies all that we’ve studied so far. This new theory also extends what
we’ve done to spaces of arbitrary (finite) dimension. It rests on the idea of differential forms.
Differential forms are hard to motivate right off the bat. It won’t be immediately clear
how differential forms are related to what we’ve done, but be patient. For now treat differential forms as a new kind of mathematical object; we’re going to learn how to manipulate
them—add, multiply, differentiate, and integrate. It will be quite abstract and “formal” at
first, but you’ll soon see how they connect with what we’ve already done.
Multivariable calculus review
Source
FORMAL CURL & DIVERGENCE
CURL
STOKES' THEOREM
DIVERGENCE
GAUSS-OSTROGRADSKY THEOREM
{d}\vec{V}=&space;\oiint_S\vec{F}\cdot{d}\vec{S})
Mathblr References
Quadratic Surfaces
Lamar University Quadratic Surfaces
