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| | | |
| ===Detail of Calculation for the Difference Map=== | | ===Detail of Calculation for the Difference Map=== |
| + | |
| + | {| 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>''' |
| + | |- style="background:ghostwhite; height:36px" |
| + | | |
| + | | <math>\operatorname{E}f|_{\operatorname{d}x\ \operatorname{d}y}</math><br><math>+ f|_{\operatorname{d}x\ \operatorname{d}y}</math> |
| + | | <math>\operatorname{E}f|_{\operatorname{d}x\ (\operatorname{d}y)}</math><br><math>+ f|_{\operatorname{d}x\ (\operatorname{d}y)}</math> |
| + | | <math>\operatorname{E}f|_{(\operatorname{d}x)\ \operatorname{d}y}</math><br><math>+ f|_{(\operatorname{d}x)\ \operatorname{d}y}</math> |
| + | | <math>\operatorname{E}f|_{(\operatorname{d}x) (\operatorname{d}y)}</math><br><math>+ f|_{(\operatorname{d}x) (\operatorname{d}y)}</math> |
| + | |- style="height:40px" |
| + | | <math>f_{0}\!</math> |
| + | | <math>0 + 0\!</math> |
| + | | <math>0 + 0\!</math> |
| + | | <math>0 + 0\!</math> |
| + | | <math>0 + 0\!</math> |
| + | |- |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | <math>f_{1}\!</math> |
| + | |- |
| + | | height="40px" | <math>f_{2}\!</math> |
| + | |- |
| + | | height="40px" | <math>f_{4}\!</math> |
| + | |- |
| + | | height="40px" | <math>f_{8}\!</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & x & y & \operatorname{d}x & \operatorname{d}y \\ |
| + | + & (x) & (y) & \operatorname{d}x & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & x & (y) & \operatorname{d}x & \operatorname{d}y \\ |
| + | + & (x) & y & \operatorname{d}x & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x) & y & \operatorname{d}x & \operatorname{d}y \\ |
| + | + & x & (y) & \operatorname{d}x & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x) & (y) & \operatorname{d}x & \operatorname{d}y \\ |
| + | + & x & y & \operatorname{d}x & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & x & (y) & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | + & (x) & (y) & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & x & y & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | + & (x) & y & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x) & (y) & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | + & x & (y) & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x) & y & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | + & x & y & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x) & y & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | + & (x) & (y) & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x) & (y) & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | + & (x) & y & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & x & y & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | + & x & (y) & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & x & (y) & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | + & x & y & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x) & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | + & (x) & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x) & y & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | + & (x) & y & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & x & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | + & x & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & x & y & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | + & x & y & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | <math>f_{3}\!</math> |
| + | |- |
| + | | height="40px" | <math>f_{12}\!</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & x & & \operatorname{d}x & \operatorname{d}y \\ |
| + | + & (x) & & \operatorname{d}x & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x) & & \operatorname{d}x & \operatorname{d}y \\ |
| + | + & x & & \operatorname{d}x & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & x & & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | + & (x) & & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x) & & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | + & x & & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x) & & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | + & (x) & & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & x & & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | + & x & & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x) & & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | + & (x) & & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & x & & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | + & x & & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | <math>f_{6}\!</math> |
| + | |- |
| + | | height="40px" | <math>f_{9}\!</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x, & y) & \operatorname{d}x & \operatorname{d}y \\ |
| + | + & (x, & y) & \operatorname{d}x & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & ((x, & y)) & \operatorname{d}x & \operatorname{d}y \\ |
| + | + & ((x, & y)) & \operatorname{d}x & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & ((x, & y)) & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | + & (x, & y) & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x, & y) & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | + & ((x, & y)) & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & ((x, & y)) & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | + & (x, & y) & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x, & y) & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | + & ((x, & y)) & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x, & y) & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | + & (x, & y) & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & ((x, & y)) & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | + & ((x, & y)) & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | <math>f_{5}\!</math> |
| + | |- |
| + | | height="40px" | <math>f_{10}\!</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & & y & \operatorname{d}x & \operatorname{d}y \\ |
| + | + & & (y) & \operatorname{d}x & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & & (y) & \operatorname{d}x & \operatorname{d}y \\ |
| + | + & & y & \operatorname{d}x & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & & (y) & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | + & & (y) & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & & y & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | + & & y & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & & y & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | + & & (y) & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & & (y) & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | + & & y & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | + & & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & & y & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | + & & y & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | <math>f_{7}\!</math> |
| + | |- |
| + | | height="40px" | <math>f_{11}\!</math> |
| + | |- |
| + | | height="40px" | <math>f_{13}\!</math> |
| + | |- |
| + | | height="40px" | <math>f_{14}\!</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & ((x) & (y)) & \operatorname{d}x & \operatorname{d}y \\ |
| + | + & (x & y) & \operatorname{d}x & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & ((x) & y) & \operatorname{d}x & \operatorname{d}y \\ |
| + | + & (x & (y)) & \operatorname{d}x & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x & (y)) & \operatorname{d}x & \operatorname{d}y \\ |
| + | + & ((x) & y) & \operatorname{d}x & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x & y) & \operatorname{d}x & \operatorname{d}y \\ |
| + | + & ((x) & (y)) & \operatorname{d}x & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & ((x) & y) & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | + & (x & y) & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & ((x) & (y)) & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | + & (x & (y)) & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x & y) & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | + & ((x) & y) & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x & (y)) & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | + & ((x) & (y)) & \operatorname{d}x & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x & (y)) & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | + & (x & y) & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x & y) & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | + & (x & (y)) & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & ((x) & (y)) & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | + & ((x) & y) & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & ((x) & y) & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | + & ((x) & (y)) & (\operatorname{d}x) & \operatorname{d}y \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x & y) & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | + & (x & y) & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & (x & (y)) & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | + & (x & (y)) & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & ((x) & y) & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | + & ((x) & y) & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |- |
| + | | height="40px" | |
| + | <math>\begin{smallmatrix} |
| + | & ((x) & (y)) & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | + & ((x) & (y)) & (\operatorname{d}x) & (\operatorname{d}y) \\ |
| + | \end{smallmatrix}</math> |
| + | |} |
| + | |- style="height:40px" |
| + | | <math>f_{15}\!</math> |
| + | | <math>1 + 1\!</math> |
| + | | <math>1 + 1\!</math> |
| + | | <math>1 + 1\!</math> |
| + | | <math>1 + 1\!</math> |
| + | |} |
| + | <br> |
| | | |
| ==Appendix 3== | | ==Appendix 3== |