Jupyter笔记本中包含的Markdown解析器支持MathJax。这意味着您可以使用 MathJax subset of Tex and LaTeXSome examples from the MathJax demos site 转载如下,以及Markdown+TeX来源。

鼓舞人心的例子#

洛伦兹方程#

来源#

\begin{align}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{align}

显示#

\(\begin{align} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{align}\)

柯西-施瓦茨不等式#

来源#

\begin{equation*}
\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
\end{equation*}

显示#

\(\begin{equation*} \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \end{equation*}\)

一个叉积公式#

来源#

\begin{equation*}
\mathbf{V}_1 \times \mathbf{V}_2 =  \begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
\frac{\partial X}{\partial u} &  \frac{\partial Y}{\partial u} & 0 \\
\frac{\partial X}{\partial v} &  \frac{\partial Y}{\partial v} & 0
\end{vmatrix}
\end{equation*}

显示#

\(\begin{equation*} \mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix} \end{equation*}\)

当抛出(N)枚硬币时得到(K)个头的概率是#

来源#

\begin{equation*}
P(E)   = {n \choose k} p^k (1-p)^{ n-k}
\end{equation*}

显示#

\(\begin{equation*} P(E) = {n \choose k} p^k (1-p)^{ n-k} \end{equation*}\)

拉马努扬的一个身份#

来源#

\begin{equation*}
\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
{1+\frac{e^{-8\pi}} {1+\ldots} } } }
\end{equation*}

显示#

\(\begin{equation*} \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } } \end{equation*}\)

罗杰斯-拉马努扬身份#

来源#

\begin{equation*}
1 +  \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
\quad\quad \text{for $|q|<1$}.
\end{equation*}

显示#

\[\begin{equation*} 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for $|q|<1$}. \end{equation*}\]

麦克斯韦方程#

来源#

\begin{align}
\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\   \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
\nabla \cdot \vec{\mathbf{B}} & = 0
\end{align}

显示#

\(\begin{align} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{align}\)

方程式编号和参考资料#

公式编号和参考将在未来版本的Jupyter笔记本中提供。

内联排版(混合Markdown和Tex)#

While display equations look good for a page of samples, the ability to mix math and formatted text in a paragraph is also important.

来源#

This expression $\sqrt{3x-1}+(1+x)^2$ is an example of a TeX inline equation in a [Markdown-formatted](https://daringfireball.net/projects/markdown/) sentence.

显示#

这个表达方式 \(\sqrt{3x-1}+(1+x)^2\) 中的TeX内联方程的示例。 Markdown-formatted 判刑。

其他语法#

你会在网上的其他地方注意到 $$ 来开始和结束MathJax排版。这是 not 如果您要使用TeX环境,则需要,但Jupyter笔记本电脑将在传统笔记本电脑上接受此语法。

来源#

$$
\begin{array}{c}
y_1 \\\
y_2 \mathtt{t}_i \\\
z_{3,4}
\end{array}
$$
$$
\begin{array}{c}
y_1 \cr
y_2 \mathtt{t}_i \cr
y_{3}
\end{array}
$$
$$\begin{eqnarray}
x' &=& &x \sin\phi &+& z \cos\phi \\
z' &=& - &x \cos\phi &+& z \sin\phi \\
\end{eqnarray}$$
$$
x=4
$$

显示#

\[\begin{split}\begin{array}{c} y_1 \\\ y_2 \mathtt{t}_i \\\ z_{3,4} \end{array}\end{split}\]
\[\begin{array}{c} y_1 \cr y_2 \mathtt{t}_i \cr y_{3} \end{array}\]
\[\begin{split}\begin{eqnarray} x' &=& &x \sin\phi &+& z \cos\phi \\ z' &=& - &x \cos\phi &+& z \sin\phi \\ \end{eqnarray}\end{split}\]
\[X=4\]