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Directory:Jon Awbrey/Papers/Differential Analytic Turing Automata (view source)
Revision as of 15:47, 11 March 2009
, 15:47, 11 March 2009→Computation Summary : <math>f(u, v) = \texttt{((u)(v))}</math>: markup
\\ \\
\\ \\
& = & & & \texttt{u(v)} \cdot \texttt{du} & + & \texttt{(u)v} \cdot \texttt{dv} & + & \texttt{(u)(v)} \cdot \texttt{(du, dv)}
& = & & & \texttt{u(v)} \cdot \texttt{du} & + & \texttt{(u)v} \cdot \texttt{dv} & + & \texttt{(u)(v)} \cdot \texttt{(du, dv)}
\end{matrix}</math>
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Figure 1.5 shows what remains of the difference map <math>\operatorname{D}f</math> when the first order linear contribution <math>\operatorname{d}f</math> is removed, namely:
{| align="center" cellpadding="8" width="90%"
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<math>\begin{matrix}
\operatorname{r}f
& = & \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}
\\ \\
& = & \texttt{du~dv}
\end{matrix}</math>
\end{matrix}</math>
|}
|}
<pre>
<pre>
o---------------------------------------o
o---------------------------------------o
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