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Directory:Jon Awbrey/Papers/Differential Propositional Calculus (view source)

Revision as of 17:03, 27 June 2008

414 bytes added ,  17:03, 27 June 2008
→‎Appendices: relabel tables
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===Propositional Forms on Two Variables===
 
===Propositional Forms on Two Variables===
   −
====Table 1====
+
====Table A1.  Propositional Forms on Two Variables====
    
{| align="center" border="1" cellpadding="0" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
 
{| align="center" border="1" cellpadding="0" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
−
|+ '''Table 1.  Propositional Forms on Two Variables'''
+
|+ '''Table A1.  Propositional Forms on Two Variables'''
 
|- style="background:ghostwhite; height:36px"
 
|- style="background:ghostwhite; height:36px"
 
| <math>\mathcal{L}_1</math>
 
| <math>\mathcal{L}_1</math>
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<br>
 
<br>
   −
====Table 2====
+
====Table A2.  Propositional Forms on Two Variables====
    
{| align="center" border="1" cellpadding="0" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
 
{| align="center" border="1" cellpadding="0" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
−
|+ '''Table 2.  Propositional Forms on Two Variables'''
+
|+ '''Table A2.  Propositional Forms on Two Variables'''
 
|- style="background:ghostwhite; height:36px"
 
|- style="background:ghostwhite; height:36px"
 
| <math>\mathcal{L}_1</math>
 
| <math>\mathcal{L}_1</math>
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<br>
 
<br>
   −
====Table 3====
+
====Table A3.  E''f'' Expanded Over Differential Features====
    
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
 
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
−
|+ '''Table 3.  <math>\operatorname{E}f</math> Expanded Over Differential Features <math>\{ \operatorname{d}x, \operatorname{d}y \}</math>'''
+
|+ '''Table A3.  <math>\operatorname{E}f</math> Expanded Over Differential Features <math>\{ \operatorname{d}x, \operatorname{d}y \}</math>'''
 
|- style="background:ghostwhite; height:48px"
 
|- style="background:ghostwhite; height:48px"
 
| &nbsp;
 
| &nbsp;
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<br>
 
<br>
   −
====Table 4====
+
====Table A4.  D''f'' Expanded Over Differential Features====
    
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
 
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
−
|+ '''Table 4.  <math>\operatorname{D}f</math> Expanded Over Differential Features <math>\{ \operatorname{d}x, \operatorname{d}y \}</math>'''
+
|+ '''Table A4.  <math>\operatorname{D}f</math> Expanded Over Differential Features <math>\{ \operatorname{d}x, \operatorname{d}y \}</math>'''
 
|- style="background:ghostwhite; height:36px"
 
|- style="background:ghostwhite; height:36px"
 
| &nbsp;
 
| &nbsp;
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<br>
 
<br>
   −
====Table 5====
+
====Table A5.  E''f'' Expanded Over Ordinary Features====
    
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
 
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
−
|+ '''Table 5.  <math>\operatorname{E}f</math> Expanded Over Ordinary Features <math>\{ x, y \}\!</math>'''
+
|+ '''Table A5.  <math>\operatorname{E}f</math> Expanded Over Ordinary Features <math>\{ x, y \}\!</math>'''
 
|- style="background:ghostwhite; height:36px"
 
|- style="background:ghostwhite; height:36px"
 
| &nbsp;
 
| &nbsp;
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<br>
 
<br>
   −
====Table 6====
+
====Table A6.  D''f'' Expanded Over Ordinary Features====
    
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
 
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
−
|+ '''Table 6.  <math>\operatorname{D}f</math> Expanded Over Ordinary Features <math>\{ x, y \}\!</math>'''
+
|+ '''Table A6.  <math>\operatorname{D}f</math> Expanded Over Ordinary Features <math>\{ x, y \}\!</math>'''
 
|- style="background:ghostwhite; height:36px"
 
|- style="background:ghostwhite; height:36px"
 
| &nbsp;
 
| &nbsp;
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===Differential Forms===
 
===Differential Forms===
   −
====Expanded on a Logical Basis====
+
====Table A7.  Differential Forms Expanded on a Logical Basis====
    
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
 
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
−
|+ '''Differential Forms Expanded on a Logical Basis'''
+
|+ '''Table A7.  Differential Forms Expanded on a Logical Basis'''
 
|- style="background:ghostwhite; height:36px"
 
|- style="background:ghostwhite; height:36px"
 
| &nbsp;
 
| &nbsp;
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<br>
 
<br>
   −
====Expanded on an Algebraic Basis====
+
====Table A8.  Differential Forms Expanded on an Algebraic Basis====
    
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
 
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
−
|+ '''Differential Forms Expanded on an Algebraic Basis'''
+
|+ '''Table A8.  Differential Forms Expanded on an Algebraic Basis'''
 
|- style="background:ghostwhite; height:36px"
 
|- style="background:ghostwhite; height:36px"
 
| &nbsp;
 
| &nbsp;
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==Appendix 3==
 
==Appendix 3==
   −
===Taylor Series Expansion===
+
===Table A9.  Taylor Series Expansion===
    
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
 
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
−
|+ '''Taylor Series Expansion <math>\operatorname{D}f = \operatorname{d}f + \operatorname{d}^2 f</math>'''
+
|+ '''Table A9.  Taylor Series Expansion <math>\operatorname{D}f = \operatorname{d}f + \operatorname{d}^2 f</math>'''
 
|- style="background:ghostwhite"
 
|- style="background:ghostwhite"
 
| &nbsp;
 
| &nbsp;
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<br>
 
<br>
   −
===Partial Differentials and Relative Differentials===
+
===Table A10.  Partial Differentials and Relative Differentials===
    
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
 
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
−
|+ '''Partial Differentials and Relative Differentials'''
+
|+ '''Table A10.  Partial Differentials and Relative Differentials'''
 
|- style="background:ghostwhite; height:48px"
 
|- style="background:ghostwhite; height:48px"
 
| &nbsp;
 
| &nbsp;
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==Appendix 4==
 
==Appendix 4==
   −
===Detail of Calculation for the Difference Map===
+
===Table A11.  Detail of Calculation for the Difference Map===
    
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
 
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
−
|+ '''Detail of Calculation for <math>\operatorname{D}f = \operatorname{E}f + f</math>'''
+
|+ '''Table A11.  Detail of Calculation for <math>\operatorname{D}f = \operatorname{E}f + f</math>'''
 
|- style="background:ghostwhite; height:60px"
 
|- style="background:ghostwhite; height:60px"
 
| &nbsp;
 
| &nbsp;
Jon Awbrey
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