[BUG] maps for vector calculus

[Martin Jackson]

At 7:07 AM -0700 4/30/04, Tevian Dray wrote:
>  > Having done this, it seems more natural
>>  to view the PDT as a special case of the (3D) Divergence Theorem.
>
>I like the analogy, but am still uncomfortable with this argument.  Green's
>Theorem really is equivalent to Stokes' Theorem; I know how to argue in both
>directions.  But the 2d and 3d divergence theorems are not equivalent in this
>sense; I don't know how to derive either one from the other except by analogy
>(or perhaps using differential forms).  Perhaps this bias reflects the
>traditional algebraic viewpoint, and one should accept the geometric argument
>of equivalence.  But I am still not convinced that the "special case" arrow
>connecting these theorems is justified.


Yes, I now agree that the links here are different.  I've done a bit 
of exploring and found that the map I made is essentially a "concept 
map" and that there is a whole industry of making concept maps.  In 
the "official" theory of concepts maps (see 
http://cmap.coginst.uwf.edu/info/ for example), each link is labeled 
with a verb so that one can read sentences in the diagram.  The link 
from Stokes's to Green's can read "reduces to special case of" and 
the link from Divergence to Planar Divergence can read "analogous 
to."   The link from curl to conservative vector field could read 
"test for."  I don't plan to include all of these labels because I 
think the result will be cluttered but I might experiment.