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\begin{document}
\chapter{���̕\���ƌ덷}

\section{�J��ԁE��Ԃ̕\�L�@}
$(a,b)$�̂悤�ȕ\�L�̂Ƃ��A�J��ԂƌĂє͈̗͂��[a,b�͋�ԂɊ܂܂�Ȃ��B

$[a,b]$�̂悤�ȕ\�L�̂Ƃ��A��ԂƌĂє͈̗͂��[a,b�͋�ԂɊ܂܂��B

$(a,b]$�̂悤�ȕ\�L�̂Ƃ��A���J�E���邢�͉E���J��ԂƌĂ�a�͋�ԂɊ܂܂�Ȃ���,b�͋�ԂɊ܂܂��B

$[a,b)$�̂悤�ȕ\�L�̂Ƃ��A���E�J���邢�͉E�J����ԂƌĂ�a�͋�ԂɊ܂܂�邪,b�͋�ԂɊ܂܂�Ȃ��B

\section{�֐��̌덷�͈͂ƃp�����[�^�̌덷�͈͂̊֌W}
����$x$�y��$y$�̑���l�����ꂼ��$a$,$b$�Ƃ�,���̌덷�͈̔͂�$\Delta a$,$\Delta b$�ŕ\�����Ƃ����,
\begin{eqnarray}
x = a \pm \Delta a \nonumber \\
y = b \pm \Delta b
\end{eqnarray}
�Ə������Ƃ��ł���.������$0 < \Delta a ,0 < \Delta b$�ł���.

������$x$��$y$�̊֐��Ƃ��Ă���킳����$z=f(x,y)=f({\bm x})$���l����.
����$z$��$z=f({\bm x})=c \pm \Delta c$�̌`�ŏ������Ƃ��ł�,$c$��$\Delta c$�͂��ꂼ��ȉ��̂悤�ɋL�q�ł���.
\begin{equation}
c = f(a,b) = f(\bm{a})
\end{equation}
\begin{eqnarray}
�덷�̐�Βl &=& \left| f({\bm a \pm \Delta a}) - f({\bm a}) \right| \nonumber \\
&=& \left| \left( f({\bm a}) \pm \frac{\partial f({\bm a})}{\partial {\bm x}} \Delta {\bm a} + \cdots \right) - f({\bm a}) \right| \nonumber \\
&=& \left| \pm \frac{\partial f({\bm a})}{\partial{\bm x}} \Delta{\bm a} \pm \cdots \right| \nonumber \\
& \simeq & \left| \pm \frac{\partial f({\bm a})}{\partial{\bm x}} \Delta{\bm a} \right| \nonumber \\
&=& \left| \pm \frac{\partial f(a,b)}{\partial x} \Delta a \pm \frac{\partial f(a,b)}{\partial y} \Delta b \right| \nonumber \\
& \leq & \left| \frac{\partial f(a,b)}{\partial x} \right| \Delta a + \left| \frac{\partial f(a,b)}{\partial y} \right| \Delta b \nonumber \\
& \equiv & \Delta c
\end{eqnarray}
������$0 < \Delta c$�ł���.
$\Delta c$ �ɂ͈ȉ��̂悤�Ȑ���������B

$z=f(x,y)=x \pm y$�̂Ƃ�,
\begin{eqnarray}
\Delta c &=& \frac{\partial f(a,b)}{\partial x} (\Delta a ) + \frac{\partial f(a,b)}{\partial y} (\Delta b) \nonumber \\
&=& \Delta a + \Delta b
\end{eqnarray}
�ƂȂ�,$z$�̐�Ό덷$\Delta c$�̓p�����[�^$x,y$�̐�Ό덷$\Delta x, \Delta y$�̘a�ƂȂ�.

$z=f(x,y)=xy$�̂Ƃ�,
\begin{eqnarray}
\Delta c &=& \frac{\partial f(a,b)}{\partial x} (\Delta a ) + \frac{\partial f(a,b)}{\partial y} (\Delta b) \nonumber \\
&=& b(\Delta a) + a(\Delta b) \nonumber \\ 
\frac{\Delta c}{c} &=& \frac{\Delta a}{a} + \frac{\Delta b}{b}
\end{eqnarray}
�ƂȂ�,$z$�̑��Ό덷$\frac{\Delta c}{c}$�̓p�����[�^$x,y$�̑��Ό덷$\frac{\Delta a}{a}, \frac{\Delta b}{b}$�̘a�ƂȂ�.

\section{���x�ɂ����̗�}
\begin{description}
\item[(i)] gfd1.f90�́A$n^2, n^3, 1/n$�ɂ��āAn��1�`10�̏ꍇ���o�͂���v���O�����ƂȂ��Ă���B 
\item[(ii)] gfd2.f90�́A0.01���ꖜ�񑫂��v���O�����ł���B�P���x�Ɣ{���x�̏ꍇ�Ō��ʂ̐��m�����قȂ��Ă���B

\end{description}

\end{document}
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%%%%%%%%            ���� (���x���t��)           %%%%%%%%
%
%\begin{eqnarray}
% \Deqlab{1.1} % ���ȏ��ł̎��ԍ�������.
%  \DP{\rho}{t} + \Ddiv (\rho \Dvect{V}) = 0.
%\end{eqnarray}
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%%%%%%%%  ���� (���ԍ���Ɨ����ď��������ꍇ)   %%%%%%%%
%
%$$
% \DP{p}{z} = \rho g.
% \eqno \textrm{(1.11)}
%$$
%
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%%%%%%%%         �Q�l���� (�{���ɏ����ꍇ)      %%%%%%%%
%
%{\bmseries �Q�l����}
%\vspace{-7mm}
%\begin{description}
% \bmem	���Җ�, 2000:
%	���Ж�, (��, ��).
%	�o�Ŏ�, 319pp.
%\end{description}
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%%%%%%%%             �}�̓\����                 %%%%%%%%
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% \caption{
%  ���o��
% }
% \Dfiglab{fig0101} % ���ȏ��̐}�̔ԍ�������,
%                   % table �̐}�̏ꍇ�� tab0101
%\end{figure}
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