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<pre>
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In our analysis of the transformation <math>F,\!</math> we carried out Step&nbsp;1 in the more familiar form <math>\operatorname{E}F = F + \operatorname{D}F,</math> and we have just reached Step&nbsp;2 in the form <math>\operatorname{D}F = \operatorname{d}F + \operatorname{r}F,</math> where <math>\operatorname{r}F</math> is the residual term that remains for us to examine next.
In our analysis of the current transformation F,
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we carried out Step 1 in the more familiar form
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EF = F + DF, and we have just reached Step 2 in
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the form DF = dF + rF, where rF is the residual
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term that remains for us to examine next.
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NB.  I'm am trying to give quick overview here,
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'''NB.''' I'm am trying to give quick overview here, and this forces me to omit many picky details. The picky reader may wish to consult the more detailed presentation of this material at the following locations:
and this forces me to omit many picky details.
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The picky reader may wish to consult the more
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detailed presentation of this material in the
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following ur-neighborhoods:
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Jon Awbrey, "Differential Logic and Dynamic Systems"
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; Jon Awbrey, "Differential Logic and Dynamic Systems"
 
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: [http://stderr.org/pipermail/inquiry/2003-May/thread.html#478 DLOG D-a].   
DLOG D.  http://stderr.org/pipermail/inquiry/2003-May/thread.html#478
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: [http://stderr.org/pipermail/inquiry/2003-June/thread.html#553 DLOG D-b].
DLOG D.  http://stderr.org/pipermail/inquiry/2003-June/thread.html#553
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; Especially
 
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: [http://stderr.org/pipermail/inquiry/2003-May/000521.html DLOG D40].
Especially:
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: [http://stderr.org/pipermail/inquiry/2003-June/000554.html DLOG D71].
 
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DLOG D40.  http://stderr.org/pipermail/inquiry/2003-May/000521.html
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DLOG D71. http://stderr.org/pipermail/inquiry/2003-June/000554.html
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Take your pick, Gimli ...
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</pre>
      
==Note 18==
 
==Note 18==
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