代表的な数式例
\[x = \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\]\[x = \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\]
\[f’(x) = \lim_{\varDelta x \to 0} \frac{ f(x+\varDelta x) - f(x) }{\varDelta x}\]\[f’(x) = \lim_{\varDelta x \to 0} \frac{ f(x+\varDelta x) – f(x) }{\varDelta x}\]
\[\dot x = dx/dt=\frac{d x(t)}{d t}=\frac{d}{d t}\left(x(t)\right)\]\[\dot x = dx/dt=\frac{d x(t)}{d t}=\frac{d}{d t}\left(x(t)\right)\]
\[\int_{-\infty}^{\infty} e^{-x^{2}} \, dx = \sqrt{\pi}\]\[\int_{-\infty}^{\infty} e^{-x^{2}} \, dx = \sqrt{\pi}\]
複数行の数式例
\begin{align}
(a+b)^2 &= a^2+2ab+b^2 \tag{1}\\
(a-b)^2 &= a^2-2ab+b^2 \tag{2}\\
(a+b)^3 &= a^3+3a^{2}b+3ab^2+b^3\tag{3}
\end{align}\begin{align}
(a+b)^2 &= a^2+2ab+b^2 \tag{1}\\
(a-b)^2 &= a^2-2ab+b^2 \tag{2}\\
(a+b)^3 &= a^3+3a^{2}b+3ab^2+b^3\tag{3}
\end{align}
\[
\left\{
\begin{align}
2x + y &= 3 \\
3x - 4y &= 1
\end{align}
\right.
\]\[
\left\{
\begin{align}
2x + y &= 3 \\
3x – 4y &= 1
\end{align}
\right.
\]
\begin{align}
\cos 2\theta &= \cos^{2} \theta - \sin^{2} \theta \\
&= 2\cos^{2} \theta - 1 \\
&= 1 - 2\sin^{2} \theta
\end{align} \begin{align}
\cos 2\theta &= \cos^{2} \theta – \sin^{2} \theta \\
&= 2\cos^{2} \theta – 1 \\
&= 1 – 2\sin^{2} \theta
\end{align}
\[
|x| = \begin{cases}
x & (x \ge 0 のとき) \\
-x & (x \lt 0 のとき)
\end{cases}
\]\[
|x| = \begin{cases}
x & (x \ge 0 のとき) \\
-x & (x \lt 0 のとき)
\end{cases}
\]
ベクトルの数式例
\\[\boldsymbol{A}\cdot\boldsymbol{B} = A_x B_x +A_y B_y +A_z B_z\]\[\boldsymbol{A}\cdot\boldsymbol{B} = A_x B_x +A_y B_y +A_z B_z\]
\[ ( a_1, a_2, \cdots , a_n ) \]\[ ( a_1, a_2, \cdots , a_n ) \]
\[a = \| \boldsymbol{a} \| = \sqrt{a_1^2 + a_2^2 + \cdots +a_n^2} \]\[a = \| \boldsymbol{a} \| = \sqrt{a_1^2 + a_2^2 + \cdots +a_n^2} \]