The Surface Integral Song
Lyrics:
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If you find an oriented surface
Stop and ask yourself "what is my purpose"
Call upon a lovely vector field
Integrate and the flux will be revealed
Deep inside your heart you'll find
Your favorite function G
Cross the partials with respect
To u and v
Double the parameters, double the fun
Double integration when it's all said and done
Double check your normal vector
It's important to respect her
Make sure that she's pointing in the right direction
(You gotta make sure she's the one)
If you come across a surface that seems spherical
Call upon theta, rho, and phi - your favorite change of variables
Write down the equation, you'll get some inspiration
And after a translation, there's your parameterization
Deep inside your heart you'll find
Your favorite function G
Cross the partials with respect
To u and v
Double the parameters, double the fun
Double integration when it's all said and done
Double check your normal vector
It's important to respect her
Make sure that she's pointing in the right direction
Double the parameters, double the fun
Double integration when it's all said and done
Double check your normal vector
It's important to respect her
Make sure that she's pointing in the right direction
(You gotta make sure she's the one)
(Don't stop until it's done)
('Cause two parameters is better than one)