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Directory:Jon Awbrey/Papers/Differential Logic and Dynamic Systems 2.0 (view source)

Revision as of 17:30, 8 September 2013

1,954 bytes added ,  17:30, 8 September 2013
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|+ '''Table 67. Computation of an Analytic Series in Terms of Coordinates'''
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|+ style="height:30px" | <math>\text{Table 67.} ~~ \text{Computation of an Analytic Series in Terms of Coordinates}\!</math>
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{| align="center" border="1" cellpadding="0" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
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| style="border-bottom:1px solid black" | <math>u\!</math>
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| style="border-bottom:1px solid black" | <math>v\!</math>
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:100%"
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| style="border-bottom:1px solid black; border-left:1px solid black" | <math>\mathrm{d}u\!</math>
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| ''u''
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| style="border-bottom:1px solid black" | <math>\mathrm{d}v\!</math>
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| ''v''
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| style="border-bottom:1px solid black; border-left:1px solid black" | <math>u'\!</math>
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| style="border-bottom:1px solid black" | <math>v'\!</math>
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| style="border-bottom:1px solid black; border-left:4px double black" | <math>f\!</math>
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:100%"
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| style="border-bottom:1px solid black" | <math>g\!</math>
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| d''u''
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| style="border-bottom:1px solid black; border-left:1px solid black" | <math>{\mathrm{E}f}\!</math>
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| d''v''
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| style="border-bottom:1px solid black" | <math>{\mathrm{E}g}\!</math>
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| style="border-bottom:1px solid black; border-left:1px solid black" | <math>{\mathrm{D}f}\!</math>
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| style="border-bottom:1px solid black" | <math>{\mathrm{D}g}\!</math>
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:100%"
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| style="border-bottom:1px solid black; border-left:1px solid black" | <math>{\mathrm{d}f}\!</math>
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| ''u''<font face="courier new">’</font>
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| style="border-bottom:1px solid black" | <math>{\mathrm{d}g}\!</math>
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| ''v''<font face="courier new">’</font>
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| style="border-bottom:1px solid black; border-left:1px solid black" | <math>{\mathrm{d}^2\!f}\!</math>
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| style="border-bottom:1px solid black" | <math>{\mathrm{d}^2\!g}\!</math>
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:100%"
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:100%"
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:100%"
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| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
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| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
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| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}0\\0\\1\\1\end{matrix}\!</math>
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| style="vertical-align:top; border-top:1px solid black" |
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<math>\begin{matrix}0\\1\\0\\1\end{matrix}\!</math>
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| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}0\\0\\1\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}0\\1\\0\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left: 4px double black" | <math>0\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}0\\1\\1\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}1\\0\\0\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}0\\1\\1\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}0\\1\\1\\0\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}0\\1\\1\\0\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}0\\1\\1\\0\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}0\\0\\0\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}0\\0\\0\\0\end{matrix}\!</math>
 
|-
 
|-
−
| 1 || 0
+
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}0\\0\\1\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}0\\1\\0\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}0\\0\\1\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}1\\0\\1\\0\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left: 4px double black" | <math>1\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}1\\0\\1\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}0\\1\\1\\0\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}0\\1\\0\\0\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}0\\1\\1\\0\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}0\\1\\0\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}0\\1\\1\\0\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}0\\0\\0\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}0\\0\\0\\0\end{matrix}\!</math>
 
|-
 
|-
−
| 1 || 1
+
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
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|}
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| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
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|
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| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
{| align="center" border="0" cellpadding="6" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
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<math>\begin{matrix}0\\0\\1\\1\end{matrix}\!</math>
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| 0 || 0
+
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}0\\1\\0\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}1\\1\\0\\0\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}0\\1\\0\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left: 4px double black" | <math>1\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}1\\1\\0\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}0\\1\\1\\0\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}0\\0\\1\\0\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}0\\1\\1\\0\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}0\\0\\1\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}0\\1\\1\\0\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}0\\0\\0\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}0\\0\\0\\0\end{matrix}\!</math>
 
|-
 
|-
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| 1 || 1
+
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
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|-
+
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
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| 1 || 1
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| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
|-
+
<math>\begin{matrix}0\\0\\1\\1\end{matrix}\!</math>
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| 1 || 0
+
| style="vertical-align:top; border-top:1px solid black" |
−
|}
+
<math>\begin{matrix}0\\1\\0\\1\end{matrix}\!</math>
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|
+
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
{| align="center" border="0" cellpadding="6" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
+
<math>\begin{matrix}1\\1\\0\\0\end{matrix}\!</math>
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| 0 || 0
+
| style="vertical-align:top; border-top:1px solid black" |
−
|-
+
<math>\begin{matrix}1\\0\\1\\0\end{matrix}\!</math>
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| 1 || 1
+
| style="vertical-align:top; border-top:1px solid black; border-left: 4px double black" | <math>1\!</math>
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|-
+
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
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| 1 || 1
+
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
|-
+
<math>\begin{matrix}1\\1\\1\\0\end{matrix}\!</math>
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| 0 || 0
+
| style="vertical-align:top; border-top:1px solid black" |
−
|}
+
<math>\begin{matrix}1\\0\\0\\1\end{matrix}\!</math>
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|
+
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
{| align="center" border="0" cellpadding="6" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
+
<math>\begin{matrix}0\\0\\0\\1\end{matrix}\!</math>
−
| 0 || 0
+
| style="vertical-align:top; border-top:1px solid black" |
−
|-
+
<math>\begin{matrix}0\\1\\1\\0\end{matrix}\!</math>
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| 0 || 0
+
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
|-
+
<math>\begin{matrix}0\\0\\0\\0\end{matrix}\!</math>
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| 0 || 0
+
| style="vertical-align:top; border-top:1px solid black" |
−
|-
+
<math>\begin{matrix}0\\1\\1\\0\end{matrix}\!</math>
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| 1 || 0
+
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
|}
+
<math>\begin{matrix}0\\0\\0\\1\end{matrix}\!</math>
−
|-
+
| style="vertical-align:top; border-top:1px solid black" |
−
| valign="top" |
+
<math>\begin{matrix}0\\0\\0\\0\end{matrix}\!</math>
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
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| 1 || 0
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|}
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
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| 1 || 0
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|}
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|
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
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| 0 || 0
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| 1 || 1
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|}
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
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| 0 || 0
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|}
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|-
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| valign="top" |
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
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|}
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
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{| align="center" border="0" cellpadding="6" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
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   Line 7,265: Line 7,072:  
{| 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:90%"
 
{| 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:90%"
 
|+ style="height:30px" | <math>\text{Table 68.} ~~ \text{Computation of an Analytic Series in Symbolic Terms}\!</math>
 
|+ style="height:30px" | <math>\text{Table 68.} ~~ \text{Computation of an Analytic Series in Symbolic Terms}\!</math>
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| <math>u\!</math>
 
| <math>u\!</math>
 
| <math>v\!</math>
 
| <math>v\!</math>
Jon Awbrey
12,080

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