在LaTeX中插入数学公式

你的名字 2022-05-14 09:40 346阅读 0赞

在论文写作的过程中,手动进行文字排版是一件繁琐的事情,我们可以使用LaTeX进行文字的排版以及数学公式的插入,可以很大地节省时间,专注于论文内容的写作.上篇博客介绍了LateX的安装.

## LaTeX公式基础 ##

这里的基础嫌烦的话可以先不看，直接看杂例，有不理解的地方在回来看这里的内容。此处知识摘取了一些简单的语法，如果需要完整的LaTeX书写数学公式的文档，见参考文献。

### 排版方式 ###

**行级元素(inline)**，行级元素使用`$...$`，两个$表示公式的首尾。

**块级元素(displayed)**，块级元素使用`$$...$$`。块级元素默认是居中显示的。

### 常用西文符号 ###

![SouthEast][]

标注:

![è¿éåå¾çæè¿°][SouthEast 1]

![è¿éåå¾çæè¿°][SouthEast 2]

### 上标与下标 ###

![SouthEast 3][]

### 集合: ###

![70][]

### 逻辑: ###

![70 1][]

### 关系符号: ###

![70 2][]

### 括号 ###

小括号和中括号直接使用，大括号由于用来分组，所以需要转义。`\{1+2\}`:\{1+2\}\{1+2\}

### 运算 ###

*  分数：`\frac{}{}`。例如，`\frac{1+1}{2}+1`: \{1+1\}/2+1
 *  求和：`\sum_1^n`:![\\sum\_\{i=1\}^n i][sum_i_1_n i]
 *  求积:   `\prod_1^n:`
 *  积分：`\int_a^b x^2`:![\\int \_a^b x^2][int _a_b x_2]
 *  极限：`\lim_{x\to\infty}`:limx→∞
 *  矩阵：`$$\begin{matrix}…\end{matrix}$$`，使用&分隔同行元素，\\\\换行。例如：

$$
            \begin{matrix}
            1 & x & x^2 \\
            1 & y & y^2 \\
            1 & z & z^2 \\
            \end{matrix}
    $$

### 矩阵各种形式: ###

![è¿éåå¾çæè¿°][SouthEast 4]

smallmatrix生成行间矩阵

![SouthEast 5][]

### 括号: ###

使用\\big \\Big \\bigg \\Bigg来调整其大小

![è¿éåå¾çæè¿°][SouthEast 6]

### 省略号: ###

![SouthEast 7][]

### 空白距离: ###

![SouthEast 8][]

## 杂例 ##

*  `$$h(\theta)=\sum_{j=0}^n \theta_j x_j$$`
 *                                                      ![h(\\theta)=\\sum\_\{j=0\}^n \\theta\_jx\_j][h_theta_sum_j_0_n _theta_jx_j](线性模型)
 *  `$$J(\theta)=\frac1{2m}\sum_{i=0}(y^i-h_\theta(x^i))^2$$`
    
     
    
                                         ![J(\\theta)=\\frac1\{2m\}\\sum\_\{i=0\}(y^i-h\_\\theta(x^i))^2][J_theta_frac1_2m_sum_i_0_y_i-h_theta_x_i_2](junfangwucha)
 *  `$$\frac{\partialJ(\theta)}{\partial\theta_j}=-\frac1m\sum_{i=0}^m(y^i-h_\theta(x^i))x^i_j $$`
    
     
    
                                                      ![\\frac\{\\partial J(\\theta)\}\{\\partial\\theta\_j\}=-\\frac\{1\}\{m\}\\sum\_\{i=0\}^m(y^i-h\_\\theta(x^i))x^i\_j][frac_partial J_theta_partial_theta_j_-_frac_1_m_sum_i_0_m_y_i-h_theta_x_i_x_i_j]
 *  分支函数

$$
    f(n) =
        \begin{cases}
        n/2,  & \text{if $n$ is even} \\
        3n+1, & \text{if $n$ is odd}
        \end{cases}
    $$

![70 3][]

*  数组

$$
    \left\{ 
        \begin{array}{c}
            a_1x+b_1y+c_1z=d_1 \\ 
            a_2x+b_2y+c_2z=d_2 \\ 
            a_3x+b_3y+c_3z=d_3
        \end{array}
    \right. 
    $$

![70 4][]

$$X=\left(
            \begin{matrix}
                x_{11} & x_{12} & \cdots & x_{1d}\\
                x_{21} & x_{22} & \cdots & x_{2d}\\
                \vdots & \vdots & \ddots & \vdots\\
                x_{m1} & x_{m2} & \cdots & x_{md}\\
            \end{matrix}
        \right)
        =\left(
             \begin{matrix}
                    x_1^T \\
                    x_2^T \\
                    \vdots\\
                    x_m^T \\
                \end{matrix}
        \right)
    $$

![70 5][]

$$
    \begin{align}
    \frac{\partial J(\theta)}{\partial\theta_j}
    & = -\frac1m\sum_{i=0}^m(y^i-h_\theta(x^i)) \frac{\partial}{\partial\theta_j}(y^i-h_\theta(x^i)) \\
    & = -\frac1m\sum_{i=0}^m(y^i-h_\theta(x^i)) \frac{\partial}{\partial\theta_j}(\sum_{j=0}^n\theta_jx_j^i-y^i) \\
    & = -\frac1m\sum_{i=0}^m(y^i-h_\theta(x^i))x^i_j
    \end{align}
    $$

![70 6][]

### 黑板粗体 ###

语法

`             \mathbf{ 012…abc…ABC…}`

效果

![\\pagecolor\{White\}\\mathbf\{0 \\ 1 \\ 2 \\ 3 \\ 4 \\ 5 \\ 6 \\ 7 \\ 8 \\ 9\}][pagecolor_White_mathbf_0 _ 1 _ 2 _ 3 _ 4 _ 5 _ 6 _ 7 _ 8 _ 9]

### 斜体数字 ###

语法

`            \mathit{ 0123456789}`

效果

![\\mathit\{0123456789\}\\!][mathit_0123456789]

### 数学字体 ###

![70 7][]

参考博客:

[https://blog.csdn.net/u011826404/article/details/70215074][https_blog.csdn.net_u011826404_article_details_70215074]

[http://www.cnblogs.com/Sinte-Beuve/p/6160905.html][http_www.cnblogs.com_Sinte-Beuve_p_6160905.html]

[https://blog.csdn.net/garfielder007/article/details/51646604][https_blog.csdn.net_garfielder007_article_details_51646604]

[SouthEast]: /images/20220514/96443ef7723145949f01633d0fbd0b04.png
[SouthEast 1]: /images/20220514/89494b646cee4c55aa9942b325ba2f6b.png
[SouthEast 2]: /images/20220514/46a388038d0b4a2cb9026f5c40e2d050.png
[SouthEast 3]: /images/20220514/8921d35a5846435d9c9ae2758a2d90d3.png
[70]: /images/20220514/6eb2a74d88bf49edac3f241e0cbee05c.png
[70 1]: /images/20220514/7bd15b1789b44ff5bcea8228e11ee922.png
[70 2]: /images/20220514/406e51b771a14b2e8c7599da5188a907.png
[sum_i_1_n i]: https://private.codecogs.com/gif.latex?%5Cdpi%7B80%7D%20%5Csum_%7Bi%3D1%7D%5En%20i
[int _a_b x_2]: https://private.codecogs.com/gif.latex?%5Cdpi%7B80%7D%20%5Cint%20_a%5Eb%20x%5E2
[SouthEast 4]: /images/20220514/83f9faa7181b48b7b3350dc60e0e3724.png
[SouthEast 5]: /images/20220514/9976c5e8c8cd4dbb92e1fc763df75af4.png
[SouthEast 6]: /images/20220514/82caf73b2a7a4ea5b8adec995f8c13c1.png
[SouthEast 7]: /images/20220514/3095bbdfa6ec4b65acf8886dcea7be9d.png
[SouthEast 8]: /images/20220514/47591c2566884b41a6fa39b9916018b6.png
[h_theta_sum_j_0_n _theta_jx_j]: https://private.codecogs.com/gif.latex?%5Cdpi%7B80%7D%20h%28%5Ctheta%29%3D%5Csum_%7Bj%3D0%7D%5En%20%5Ctheta_jx_j
[J_theta_frac1_2m_sum_i_0_y_i-h_theta_x_i_2]: https://private.codecogs.com/gif.latex?%5Cdpi%7B80%7D%20J%28%5Ctheta%29%3D%5Cfrac1%7B2m%7D%5Csum_%7Bi%3D0%7D%28y%5Ei-h_%5Ctheta%28x%5Ei%29%29%5E2
[frac_partial J_theta_partial_theta_j_-_frac_1_m_sum_i_0_m_y_i-h_theta_x_i_x_i_j]: https://private.codecogs.com/gif.latex?%5Cdpi%7B80%7D%20%5Cfrac%7B%5Cpartial%20J%28%5Ctheta%29%7D%7B%5Cpartial%5Ctheta_j%7D%3D-%5Cfrac%7B1%7D%7Bm%7D%5Csum_%7Bi%3D0%7D%5Em%28y%5Ei-h_%5Ctheta%28x%5Ei%29%29x%5Ei_j
[70 3]: /images/20220514/4472cf2864c34e4bb010c8b9f3fb07d4.png
[70 4]: /images/20220514/a8cf50985a8e4f0aa40357e8ffd01c24.png
[70 5]: /images/20220514/53e24d90ab2948d2b752887ea2289985.png
[70 6]: /images/20220514/0adff659eed24997a27617f649129ee5.png
[pagecolor_White_mathbf_0 _ 1 _ 2 _ 3 _ 4 _ 5 _ 6 _ 7 _ 8 _ 9]: /images/20220514/b687ab97792b4cd9a83e4613e3ba5d41.png
[mathit_0123456789]: /images/20220514/fe50ad9931c64278b95bd492388b845e.png
[70 7]: /images/20220514/d136fe068c824f1a94516de66493b963.png
[https_blog.csdn.net_u011826404_article_details_70215074]: https://blog.csdn.net/u011826404/article/details/70215074
[http_www.cnblogs.com_Sinte-Beuve_p_6160905.html]: http://www.cnblogs.com/Sinte-Beuve/p/6160905.html
[https_blog.csdn.net_garfielder007_article_details_51646604]: https://blog.csdn.net/garfielder007/article/details/51646604