[Phys-L] Re: geometric interpretation of partial derivatives

[jsd at AV8N.COM (John Denker)]

Aaargh!

The document I put on the website yesterday didn't include the best
part, the part about an explicitly geometric/algebraic representation
of the partial derivative in terms of little cells in space.

The punch line is
   http://www.av8n.com/physics/partial-derivative.htm#eq-pd-geom
i.e.

      ∂G                    dG ∧ dR ∧ dY
     ----(constant R, Y) = -------------
      ∂B                    dB ∧ dR ∧ dY

and the figure depicting the geometric significance of this is:
   http://www.av8n.com/physics/partial-derivative.htm#fig-tube-contours

I'm sorry to make y'all fetch the web page twice, but at least you don't
need to read it twice;  the 'new' part is
   http://www.av8n.com/physics/partial-derivative.htm#sec-wedge-ratio
and the rest is virtually unchanged.