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Revision as of 19:28, 10 March 2009
, 19:28, 10 March 2009→Note 16: markup
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Figure 1.4. df = linear approx to Df
Figure 1.4. df = linear approx to Df
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Figure 2.4. illustrates one way of ranging over the cells of the
Figure 2.4 illustrates one way of ranging over the cells of the underlying universe <math>U^\circ = [u, v]\!</math> and selecting at each cell the linear proposition in <math>\operatorname{d}U^\circ = [du, dv]</math> that best approximates the patch of the difference map <math>\operatorname{D}g</math> that is located there, yielding the following formula for the differential <math>\operatorname{d}g.</math>
underlying universe U% = [u, v] and selecting at each cell the
linear proposition in dU% = [du, dv] that best approximates
the patch of the difference map Dg that is located there,
yielding the following formula for the differential dg.
{| align="center" cellpadding="8" width="90%"
| <math>\operatorname{d}g ~=~ \texttt{uv} \cdot \texttt{(du, dv)} ~+~ \texttt{u(v)} \cdot \texttt{(du, dv)} ~+~ \texttt{(u)v} \cdot \texttt{(du, dv)} ~+~ \texttt{(u)(v)} \cdot \texttt{(du, dv)}</math>
|}
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Figure 2.4. dg = linear approx to Dg
Figure 2.4. dg = linear approx to Dg
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Well, g, that was easy, seeing as how Dg
Well, <math>g,\!</math> that was easy, seeing as how <math>\operatorname{D}g</math> is already linear at each locus, <math>\operatorname{d}g = \operatorname{D}g.</math>
is already linear at each locus, dg = Dg.
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==Note 17==
==Note 17==
