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\begin{document}
{\Large $<$ \LaTeX 文書のサンプル２$>$}\vspace{7mm}\\
\noindent{\large{\bf 例1}}
\begin{minipage}[t]{65mm}
２変数関数
$$f(x,y)=2.5-0.6x^{2}+0.8xy-0.3y^2$$
に対し、$z=f(x,y)$のグラフは空間における曲面を表す。今
$$x_{1}=0.8, \ \ x_{2}=1.8, \ \
y_{1}=1.5, \ \ y_{2}=3 $$
のとき、領域
$$ {\rm D} = \left\{(x,y):x_{1} \leqq x \leqq x_{2},\ y_{1} \leqq y \leqq y_{2}
\right\} $$
における$z=f(x,y)$のグラフが右図である。
\end{minipage}
\hspace{4mm}
\begin{minipage}[t]{40mm}
\vspace{-2mm}
\epsfile{file=3d1.eps,scale=0.75}
\end{minipage}\vspace{3mm}\\
\noindent{\large{\bf 例2}}\ \ (行列の積)\vspace{-3mm}\\
$$
\left( \begin{array}{c}
a_{11} \ \ \cdots \ \ a_{1m} \\
\vdots \hspace{17mm} \vdots \vspace{0.5mm}\\
\fbox{\raisebox{0mm}[4mm][2mm]{ $a_{i1} \hspace{2.6mm} \cdots \hspace{3.3mm}
a_{im}$\hspace{0.5mm}}}
\vspace{0.4mm}\\ \vdots \hspace{17mm} \vdots \\
a_{n1} \ \ \cdots \ \ a_{nm}
\end{array} \right)
\left( \!\!\!\begin{array}{rrrrr}
{\begin{array}{c}b_{11} \\\\ \vdots \\\\ b_{m1} \end{array}}\hspace{-2mm}
& \hspace{-4mm}{\begin{array}{c} \cdots \\\\\\\\ \cdots \end{array}}
\hspace{-2mm}
& \!\!\fbox{\raisebox{0mm}[15mm][13mm]{\!\!$\begin{array}{c} b_{1j} \\\\ \vdots
\\\\ b_{mj} \end{array}$\hspace{-2mm}}}\hspace{-2mm}
& \!\!{\begin{array}{c} \cdots \\\\\\\\ \cdots \end{array}}\hspace{-2mm}
& \hspace{-4mm}{\begin{array}{c} b_{1\ell} \\\\ \vdots \\\\ b_{m\ell}
\end{array}} \end{array} \hspace{-3mm}\right)
= \left( \!\begin{array}{ccccc}
c_{11} & \hspace{-2mm}\cdots \hspace{-2mm}& c_{1j} & \hspace{-2mm} \cdots
\hspace{-2mm} & c_{1\ell}\\
\vdots &\hspace{-4mm}& \vdots &\hspace{-4mm}& \vdots \\ c_{i1} &
\hspace{-2mm}\cdots\hspace{-2mm} & c_{ij} & \hspace{-2mm}\cdots\hspace{-2mm}
& c_{i\ell}\\
\vdots &\hspace{-4mm} & \vdots &\hspace{-4mm} & \vdots \\
c_{m1} & \hspace{-2mm}\cdots\hspace{-2mm} & c_{mj} & \hspace{-2mm}\cdots
\hspace{-2mm} & c_{m\ell}
\end{array}\hspace{-1mm} \right)
$$
\hspace{3mm}ここで\vspace{-8mm}\\
$$
c_{ij}=\big( a_{i1}\ a_{i2}\ \cdots \ a_{im} \big)
\left( \hspace{-1mm}\begin{array}{c} b_{1j}\\ b_{2j} \\ \vdots \\ b_{mj} \end{ar
ray}\hspace{-1mm} \right) = a_{i1}b_{1j}+a_{i2}b_{2j}+\cdots + a_{im}b_{mj}
$$
\noindent{\large{\bf 例3}}\ \ (ベクトル)\\
\hspace{3mm}
\begin{minipage}[t]{145mm}
\begin{minipage}[l]{73mm}
長さと向きを持った有向線分を{\bf ベクトル}という。
点Aを始点、点Bを終点とする\vspace{0.5mm}\\
ベクトルを記号$\overrightarrow{\mathstrut \hspace{0.1mm}\mbox{AB}\hspace{0.8mm}}
$で表す。ベクトルを表すのに
$$
\overrightarrow{\mathstrut a}, \ \overrightarrow{\mathstrut b}, \
\overrightarrow{\mathstrut c}, \ \cdots
$$
等の記号や、斜体の太文字
$$
\mbox{\boldmath {$a$}}, \ \mbox{\boldmath {$b$}}, \ \mbox{\boldmath {$c$}},
\ \cdots
$$
等を用いる。
\end{minipage}\hspace{5mm}
\begin{minipage}[r]{50mm}
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\put(10,0){\thicklines{\vector(0,1){49}}}
\put(10,10){\thicklines{\vector(2,1){20}}}
\put(10,10){\thicklines{\vector(1,2){10}}}
\put(5,5){\makebox(5,5)[c]{O}}
\put(45,5){\makebox(5,5)[r]{$x$}}
\put(5,45){\makebox(5,5)[c]{$y$}}
\put(17.5,5){\makebox(5,5)[c]{1}}
\put(27.5,5){\makebox(5,5)[c]{2}}
\put(37.5,5){\makebox(5,5)[c]{3}}
\put(5,18){\makebox(5,5)[c]{1}}
\put(5,28){\makebox(5,5)[c]{2}}
\put(5,38){\makebox(5,5)[c]{3}}
\put(24,11){\makebox(5,5)[c]{$\overrightarrow{\mathstrut a}$}}
\put(12,23){\makebox(5,5)[c]{$\overrightarrow{\mathstrut b}$}}
\multiput(20,10)(0,2){19}{\line(0,1){0.5}}
\multiput(30,10)(0,2){19}{\line(0,1){0.5}}
\multiput(40,10)(0,2){19}{\line(0,1){0.5}}
\multiput(10,20)(2,0){19}{\line(1,0){0.5}}
\multiput(10,30)(2,0){19}{\line(1,0){0.5}}
\multiput(10,40)(2,0){19}{\line(1,0){0.5}}
\end{picture}
\end{minipage}\vspace{3mm}\\
\end{minipage}
\noindent{\large{\bf 問}}\ \ 右上図の中に$\overrightarrow{\mathstrut a}
+\overrightarrow{\mathstrut b}$を作図せよ。
\end{document}
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Copyright (C) 1999, Masaaki Inoue
許可無しに転載・複製することを禁じます。