12,080
edits
Changes
MyWikiBiz, Author Your Legacy — Wednesday May 08, 2024
Jump to navigationJump to searchDirectory:Jon Awbrey/Papers/Differential Logic and Dynamic Systems 2.0 (view source)
Revision as of 03:30, 30 August 2013
, 03:30, 30 August 2013update
<br>
<br>
{| align="center" cellpadding="6" cellspacing="0" style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; text-align:center; width:70%"
{| align="center" border="1" cellpadding="0" cellspacing="0" style="font-weight:bold; text-align:center; width:70%"
|+ style="height:30px" | <math>\text{Table 51.} ~~ \text{Computation of an Analytic Series in Symbolic Terms}\!</math>
|- style="height:35px; background:ghostwhite; width:100%"
| <math>u\!</math>
| <math>v\!</math>
| ''u'' || ''v''
| style="border-left:1px solid black" | <math>J\!</math>
| style="border-left:1px solid black" | <math>\mathrm{E}J\!</math>
| style="border-left:1px solid black" | <math>\mathrm{D}J\!</math>
| style="border-left:1px solid black" | <math>\mathrm{d}J\!</math>
| style="border-left:1px solid black" | <math>\mathrm{d}^2\!J\!</math>
|}
{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:100%"
|
| d''J''
|}
|
| d<sup>2</sup>''J''
|}
|}
|
|}
|
| d''u'' d''v''
|
| d''u'' d''v''
|-
|-
| d''u''
| style="border-top:1px solid black" |
|-
<math>\begin{matrix}
| d''v''
0
\\[4pt]
0
\\[4pt]
1
{| align="center" border="0" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
\\[4pt]
1
\end{matrix}</math>
| style="border-top:1px solid black" |
<math>\begin{matrix}
0
\\[4pt]
1
\\[4pt]
0
\\[4pt]
1
\end{matrix}</math>
| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
0
\\[4pt]
0
\\[4pt]
0
\\[4pt]
1
\end{matrix}</math>
| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
\texttt{~} \mathrm{d}u \!\;\cdot\;\! \mathrm{d}v \texttt{~}
\\[4pt]
\texttt{~} \mathrm{d}u \texttt{~(} \mathrm{d}v \texttt{)}
\\[4pt]
\texttt{(} \mathrm{d}u \texttt{)~} \mathrm{d}v \texttt{~}
\\[4pt]
\texttt{(} \mathrm{d}u \texttt{)(} \mathrm{d}v \texttt{)}
\end{matrix}</math>
| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
\texttt{~} \mathrm{d}u \!\;\cdot\;\! \mathrm{d}v \texttt{~}
\\[4pt]
\texttt{~} \mathrm{d}u \texttt{~(} \mathrm{d}v \texttt{)}
\\[4pt]
\texttt{(} \mathrm{d}u \texttt{)~} \mathrm{d}v \texttt{~}
\\[4pt]
\texttt{((} \mathrm{d}u \texttt{)(} \mathrm{d}v \texttt{))}
\end{matrix}</math>
| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
0
\\[4pt]
\mathrm{d}u
\\[4pt]
\mathrm{d}v
\\[4pt]
\texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
\end{matrix}\!</math>
| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
\mathrm{d}u \cdot \mathrm{d}v
\\[4pt]
\mathrm{d}u \cdot \mathrm{d}v
\\[4pt]
\mathrm{d}u \cdot \mathrm{d}v
\\[4pt]
\mathrm{d}u \cdot \mathrm{d}v
\end{matrix}</math>
|}
|}
<br>
<br>
