Math 21a, Fall 2008
Exhibits page Math 21a 2008, Multivariable Calculus
Rap Lyrics on Line and Flux integrals
Course head: Oliver Knill
Office: SciCtr 434

Integrals rap lyrics

by Shannon Cleary, class of 2012
So you got a line integral, how should you proceed?
Is it conservative? Yes indeed.
Just use the line integral's fundamental theorem.
Makes it easy as pie - there's no need to fear 'em.
Fundamental theorem? That sounds wack!
Nah, just find little f and then subtract!
But what about a non-conserved son of a gun?
You got some options, just gotta figure out which one.
Is it closed? That's the question you should ask.
If not then direct integration is your task.
But if it is then there's no need for tensions.
Just gotta figure out the dimensions.
2D - That's Green's, no need to cry.
Do the integral of Qx-Py.
Last up for the 3D is Stokes and don't hate.
Just curl F and dot with the normal then integrate.
Now line integrals don't seem bad,
But a rap about math - kinda sad.

A flux integral sounds kinda tricky,
Like it could get you in situations that are sticky.
But if you follow my rules you will do great.
You'll know exactly how to integrate!
First if it's a vector field that's been curled, 
Do some Stokes, easiest thing in the world.
Once the curl of F and the normal have been dotted, 
Just integrate to find the answer that's allotted.
But what if that vector field wasn't a curl?
Sounds so hard that I think I'm gunna hurl.
Nah, just ask yourself if F is open.
If so do it directly and no mopin'
Otherwise you can do a little divergence.
Then triple integrate when you get the chance.
And what if I think divergence is more fun?
Then close it up and subtract that when you're done.
Before I thought I hated flux.
Now I'm just like flux - aw shucks!   


Hear also the rap by Michael Shen
Questions and comments to
Math21b | Math 21a | Fall 2008 | Department of Mathematics | Faculty of Art and Sciences | Harvard University