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21: Errata

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Subsection 19.25(iii)

The constraint $(x,y)\neq(0,0)$ was added to the first sentence of this section.

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Equation (2.7.25)

2.7.25

\mathcal{V}_{a_{j},x}\left(F\right)=\left|\int_{a_{j}}^{x}\left|\frac{1}{f^{1/% 4}(t)}\frac{{\mathrm{d}}^{2}}{{\mathrm{d}t}^{2}}\left(\frac{1}{f^{1/4}(t)}% \right)-\frac{g(t)}{f^{1/2}(t)}\right|\,\mathrm{d}t\right|

The integrand was corrected so that the absolute value does not include the differential. Also an absolute value was introduced on the right-hand side to ensure a non-negative value for $\mathcal{V}_{a_{j},x}\left(F\right)$ .

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Table 3.5.21

The correct corner coordinates for the 9-point square, given on the last line of this table, are $(\pm\sqrt{\tfrac{3}{5}}h,\pm\sqrt{\tfrac{3}{5}}h)$ . Originally they were given incorrectly as $(\pm\sqrt{\tfrac{3}{5}}h,0)$ , $(\pm\sqrt{\tfrac{3}{5}}h,0)$ .

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Diagram	$(x_{j},y_{j})$	$w_{j}$
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$(0,0)$	$\tfrac{16}{81}$	$O\left(h^{6}\right)$
$(\pm\sqrt{\tfrac{3}{5}}h,0)$ , $(0,\pm\sqrt{\tfrac{3}{5}}h)$	$\tfrac{10}{81}$
$(\pm\sqrt{\tfrac{3}{5}}h,\pm\sqrt{\tfrac{3}{5}}h)$	$\tfrac{25}{324}$

Reported 2014-01-13 by Stanley Oleszczuk.

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Chapters 8, 20, 36

Several new equations have been added. See (8.17.24), (20.7.34), §20.11(v), (26.12.27), (36.2.28), and (36.2.29).

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References

Bibliographic citations were added in §§1.13(v), 10.14, 10.21(ii), 18.15(v), 18.32, 30.16(iii), 32.13(ii), and as general references in Chapters 19, 20, 22, and 23.

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