Latex使用手册记录

入门可以看一下下面的部分内容

1.LaTeX软件的安装和使用 
方法A（自助）：在MikTeX的官网下载免费的MikTeX编译包（150Mb）并安装。下载WinEdt（9.5Mb）（收费）或TexMaker（32Mb)（免费）等编辑界面软件并安装。 
方法B（打包）：在ctex.org下载ctex套装(203Mb或1.3Gb)（含MikTeX及WinEdt）

哈哈这一部分当然不包含在标题的30分钟里。

新人不必纠结软件问题，随便什么软件随便什么版本只要下载下来能编译出pdf来就可以，先下载了装上来试试再说。我推荐winedt也是方便我在介绍按钮样子的时候可以统一描述。在真正开始跑步之前没有必要纠结该买NIKE跑鞋还是ADI跑鞋，跑起来再说。不要瞻前顾后，just try it.

2.第一个文档 
打开WinEdt，建立一个新文档，将以下内容复制进入文档中，保存，保存类型选择为UTF-8。 

\documentclass{article} 
$$\begin{document}    hello, world  \end{document}$$  

然后在WinEdt的工具栏中找到编译按钮（在垃圾桶和字母B中间），在下拉菜单中选择XeLaTeX，并点击编译。 (这里请注意一下我之前一直笔误写的XeTeX，给大家带来困扰深感歉意） 
如果顺利的话，我们就可以顺利生成出第一个pdf文件，点击工具栏中的放大镜按钮就可以快速打开生成的pdf文件。 


3.标题、作者和注释 
建立一个新文档，将以下内容复制进入文档中，保存，保存类型选择为UTF-8，编译并观察现象。 

\documentclass{article} 
  \author{My Name} 
  \title{The Title} 
$$\begin{document}    \maketitle    hello, world % This is comment  \end{document}$$

%为本行右边所有内容被注释掉，在生成的pdf中不会显示。

块注释也有专门的语句，不过更方便的方式是选中一块区域点鼠标右键，点comment 


4.章节和段落 
建立一个新文档，将以下内容复制进入文档中，保存，保存类型选择为UTF-8，编译并观察现象。 

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<span class="pln">\documentclass</span><span class="pun">{</span><span class="pln">article</span><span class="pun">}</span><span class="pln">   \title</span><span class="pun">{</span><span class="typ">Hello</span><span class="pln"> </span><span class="typ">World</span><span class="pun">}</span><span class="pln"> \begin</span><span class="pun">{</span><span class="pln">document</span><span class="pun">}</span><span class="pln">   \maketitle   \section</span><span class="pun">{</span><span class="typ">Hello</span><span class="pln"> </span><span class="typ">China</span><span class="pun">}</span><span class="pln"> </span><span class="typ">China</span><span class="pln"> </span><span class="kwd">is</span><span class="pln"> </span><span class="kwd">in</span><span class="pln"> </span><span class="typ">East</span><span class="pln"> </span><span class="typ">Asia</span><span class="pun">.</span><span class="pln">     \subsection</span><span class="pun">{</span><span class="typ">Hello</span><span class="pln"> </span><span class="typ">Beijing</span><span class="pun">}</span><span class="pln"> </span><span class="typ">Beijing</span><span class="pln"> </span><span class="kwd">is</span><span class="pln"> the capital of </span><span class="typ">China</span><span class="pun">.</span><span class="pln">       \subsubsection</span><span class="pun">{</span><span class="typ">Hello</span><span class="pln"> </span><span class="typ">Dongcheng</span><span class="pln"> </span><span class="typ">District</span><span class="pun">}</span><span class="pln">         \paragraph</span><span class="pun">{</span><span class="typ">Tian</span><span class="str">'anmen Square}is in the center of Beijing           \subparagraph{Chairman Mao} is in the center of Tian'</span><span class="pln">anmen </span><span class="typ">Square</span><span class="pln">       \subsection</span><span class="pun">{</span><span class="typ">Hello</span><span class="pln"> </span><span class="typ">Guangzhou</span><span class="pun">}</span><span class="pln">         \paragraph</span><span class="pun">{</span><span class="typ">Sun</span><span class="pln"> </span><span class="typ">Yat</span><span class="pun">-</span><span class="pln">sen </span><span class="typ">University</span><span class="pun">}</span><span class="pln"> </span><span class="kwd">is</span><span class="pln"> the best university </span><span class="kwd">in</span><span class="pln"> </span><span class="typ">Guangzhou</span><span class="pun">.</span><span class="pln"> \end</span><span class="pun">{</span><span class="pln">document</span><span class="pun">}</span><span class="pln"> </span>

　　

退格只是我个人偏好，看起来层次清晰美观。实际操作上未必要如此，每一行之前的空格不影响编译生成PDF的排版结果。 


5.加入目录 
建立一个新文档，将以下内容复制进入文档中，保存，保存类型选择为UTF-8，编译并观察现象。 

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1 2 3 4 5 6 7 8 9

<span class="pln">\documentclass</span><span class="pun">{</span><span class="pln">article</span><span class="pun">}</span><span class="pln"> \begin</span><span class="pun">{</span><span class="pln">document</span><span class="pun">}</span><span class="pln">   \tableofcontents   \section</span><span class="pun">{</span><span class="typ">Hello</span><span class="pln"> </span><span class="typ">China</span><span class="pun">}</span><span class="pln"> </span><span class="typ">China</span><span class="pln"> </span><span class="kwd">is</span><span class="pln"> </span><span class="kwd">in</span><span class="pln"> </span><span class="typ">East</span><span class="pln"> </span><span class="typ">Asia</span><span class="pun">.</span><span class="pln">     \subsection</span><span class="pun">{</span><span class="typ">Hello</span><span class="pln"> </span><span class="typ">Beijing</span><span class="pun">}</span><span class="pln"> </span><span class="typ">Beijing</span><span class="pln"> </span><span class="kwd">is</span><span class="pln"> the capital of </span><span class="typ">China</span><span class="pun">.</span><span class="pln">       \subsubsection</span><span class="pun">{</span><span class="typ">Hello</span><span class="pln"> </span><span class="typ">Dongcheng</span><span class="pln"> </span><span class="typ">District</span><span class="pun">}</span><span class="pln">         \paragraph</span><span class="pun">{</span><span class="typ">Hello</span><span class="pln"> </span><span class="typ">Tian</span><span class="str">'anmen Square}is in the center of Beijing           \subparagraph{Hello Chairman Mao} is in the center of Tian'</span><span class="pln">anmen </span><span class="typ">Square</span><span class="pln"> \end</span><span class="pun">{</span><span class="pln">document</span><span class="pun">}</span><span class="pln"> </span>

　　

6.换行 
建立一个新文档，将以下内容复制进入文档中，保存，保存类型选择为UTF-8，编译并观察对比现象。 

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

<span class="pln">\documentclass</span><span class="pun">{</span><span class="pln">article</span><span class="pun">}</span><span class="pln"> \begin</span><span class="pun">{</span><span class="pln">document</span><span class="pun">}</span><span class="pln">   </span><span class="typ">Beijing</span><span class="pln"> </span><span class="kwd">is</span><span class="pln">   the capital   of </span><span class="typ">China</span><span class="pun">.</span><span class="pln">     </span><span class="typ">Washington</span><span class="pln"> </span><span class="kwd">is</span><span class="pln">     the capital     of </span><span class="typ">America</span><span class="pun">.</span><span class="pln">     </span><span class="typ">Amsterdam</span><span class="pln"> </span><span class="kwd">is</span><span class="pln"> \\ the capital \\   of </span><span class="typ">Netherlands</span><span class="pun">.</span><span class="pln"> \end</span><span class="pun">{</span><span class="pln">document</span><span class="pun">}</span>

　　

空一行为另起一段，\\为段内强制换行。

我对之前手滑写出New York is the capital of America这类低级错误表示非常抱歉。

7.数学公式 
建立一个新文档，将以下内容复制进入文档中，保存，保存类型选择为UTF-8，编译并观察对比现象。 

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<span class="pln">\documentclass</span><span class="pun">{</span><span class="pln">article</span><span class="pun">}</span><span class="pln">   \usepackage</span><span class="pun">{</span><span class="pln">amsmath</span><span class="pun">}</span><span class="pln">   \usepackage</span><span class="pun">{</span><span class="pln">amssymb</span><span class="pun">}</span><span class="pln"> \begin</span><span class="pun">{</span><span class="pln">document</span><span class="pun">}</span><span class="pln">   </span><span class="typ">The</span><span class="pln"> </span><span class="typ">Newton</span><span class="str">'s second law is F=ma.     The Newton'</span><span class="pln">s second law </span><span class="kwd">is</span><span class="pln"> $F</span><span class="pun">=</span><span class="pln">ma$</span><span class="pun">.</span><span class="pln">     </span><span class="typ">The</span><span class="pln"> </span><span class="typ">Newton</span><span class="str">'s second law is      F=maF=ma        The Newton'</span><span class="pln">s second law </span><span class="kwd">is</span><span class="pln">      F</span><span class="pun">=</span><span class="pln">maF</span><span class="pun">=</span><span class="pln">ma        </span><span class="typ">Greek</span><span class="pln"> </span><span class="typ">Letters</span><span class="pln"> $\eta$ </span><span class="kwd">and</span><span class="pln"> $\mu$     </span><span class="typ">Fraction</span><span class="pln"> $\frac</span><span class="pun">{</span><span class="pln">a</span><span class="pun">}{</span><span class="pln">b</span><span class="pun">}</span><span class="pln">$     </span><span class="typ">Power</span><span class="pln"> $a</span><span class="pun">^</span><span class="pln">b$     </span><span class="typ">Subscript</span><span class="pln"> $a_b$     </span><span class="typ">Derivate</span><span class="pln"> $\frac</span><span class="pun">{</span><span class="pln">\partial y</span><span class="pun">}{</span><span class="pln">\partial t</span><span class="pun">}</span><span class="pln"> $     </span><span class="typ">Vector</span><span class="pln"> $\vec</span><span class="pun">{</span><span class="pln">n</span><span class="pun">}</span><span class="pln">$     </span><span class="typ">Bold</span><span class="pln"> $\mathbf</span><span class="pun">{</span><span class="pln">n</span><span class="pun">}</span><span class="pln">$     </span><span class="typ">To</span><span class="pln"> time differential $\dot</span><span class="pun">{</span><span class="pln">F</span><span class="pun">}</span><span class="pln">$     </span><span class="typ">Matrix</span><span class="pln"> </span><span class="pun">(</span><span class="pln">lcr here means left</span><span class="pun">,</span><span class="pln"> center </span><span class="kwd">or</span><span class="pln"> right </span><span class="kwd">for</span><span class="pln"> each column</span><span class="pun">)</span><span class="pln">   \[     \left</span><span class="pun">[</span><span class="pln">       \begin</span><span class="pun">{</span><span class="pln">array</span><span class="pun">}{</span><span class="pln">lcr</span><span class="pun">}</span><span class="pln">         a1 </span><span class="pun">&</span><span class="pln"> b22 </span><span class="pun">&</span><span class="pln"> c333 \\         d444 </span><span class="pun">&</span><span class="pln"> e555555 </span><span class="pun">&</span><span class="pln"> f6       \end</span><span class="pun">{</span><span class="pln">array</span><span class="pun">}</span><span class="pln">     \right</span><span class="pun">]</span><span class="pln">   \]   </span><span class="typ">Equations</span><span class="pun">(</span><span class="pln">here \& </span><span class="kwd">is</span><span class="pln"> the symbol </span><span class="kwd">for</span><span class="pln"> aligning different rows</span><span class="pun">)</span><span class="pln"> \begin</span><span class="pun">{</span><span class="pln">align</span><span class="pun">}</span><span class="pln">   a</span><span class="pun">+</span><span class="pln">b</span><span class="pun">&=</span><span class="pln">c\\   d</span><span class="pun">&=</span><span class="pln">e</span><span class="pun">+</span><span class="pln">f</span><span class="pun">+</span><span class="pln">g \end</span><span class="pun">{</span><span class="pln">align</span><span class="pun">}</span><span class="pln">   \[   \left\{     \begin</span><span class="pun">{</span><span class="pln">aligned</span><span class="pun">}</span><span class="pln">       </span><span class="pun">&</span><span class="pln">a</span><span class="pun">+</span><span class="pln">b</span><span class="pun">=</span><span class="pln">c\\       </span><span class="pun">&</span><span class="pln">d</span><span class="pun">=</span><span class="pln">e</span><span class="pun">+</span><span class="pln">f</span><span class="pun">+</span><span class="pln">g     \end</span><span class="pun">{</span><span class="pln">aligned</span><span class="pun">}</span><span class="pln">   \right</span><span class="pun">.</span><span class="pln"> \]   \end</span><span class="pun">{</span><span class="pln">document</span><span class="pun">}</span><span class="pln"> </span>

　　

具体细节可以自行搜索LaTeX的数学符号表或别人给的例子。

 

$...$是开启行内数学模式，用于和文本合在一起使用。

 

和

......

是另起一行居中开启数学模式。通常用起来差别不是很大，不过$$会修改默认的公式行间距，有时可能会对文章的整体效果有影响。

 

有一些网站可以通过画图的方式来生成公式，有的编辑器集成了各种数学功能按钮。这对于公式需求少的人来说很方便，具体信息可以自己去搜索。但是如果你的文章中要出现大段的证明过程，就会发觉还是老老实实地google一篇latex数学符号表，然后不懂的去查代码，自己用手指敲来得干脆利索。再进阶一点，可以去搜一下有关LaTeX的自定义command的内容去看一下，在敲公式时能省很多力气。

8.插入图片 
将待插入的图片姑且先命名为figure1.jpg 
建立一个新文档，将以下内容复制进入文档中，保存，保存类型选择为UTF-8，放在和图片文件同一个文件夹里，编译并观察现象。 

\documentclass{article} 
  \usepackage{graphicx} 
\begin{document} 
  \includegraphics[width=4.00in,height=3.00in]{figure1.jpg} 
\end{document}

 

在老版本的LaTeX中是只支持eps图片格式的，现在的LaTeX对jpg、bmp、png等等常见图片都可以支持。

9.简单表格 
建立一个新文档，将以下内容复制进入文档中，保存，保存类型选择为UTF-8，编译并观察对比现象。 

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

<span class="pln">\documentclass</span><span class="pun">{</span><span class="pln">article</span><span class="pun">}</span><span class="pln"> \begin</span><span class="pun">{</span><span class="pln">document</span><span class="pun">}</span><span class="pln">   \begin</span><span class="pun">{</span><span class="pln">tabular</span><span class="pun">}{|</span><span class="pln">c</span><span class="pun">|</span><span class="pln">c</span><span class="pun">|}</span><span class="pln">     aaa </span><span class="pun">&</span><span class="pln"> b \\     c </span><span class="pun">&</span><span class="pln"> ddddd\\   \end</span><span class="pun">{</span><span class="pln">tabular</span><span class="pun">}</span><span class="pln">     \begin</span><span class="pun">{</span><span class="pln">tabular</span><span class="pun">}{|</span><span class="pln">l</span><span class="pun">|</span><span class="pln">r</span><span class="pun">|}</span><span class="pln">     \hline     aaaa </span><span class="pun">&</span><span class="pln"> b \\     \hline     c </span><span class="pun">&</span><span class="pln"> ddddd\\     \hline   \end</span><span class="pun">{</span><span class="pln">tabular</span><span class="pun">}</span><span class="pln">     \begin</span><span class="pun">{</span><span class="pln">center</span><span class="pun">}</span><span class="pln">     \begin</span><span class="pun">{</span><span class="pln">tabular</span><span class="pun">}{|</span><span class="pln">c</span><span class="pun">|</span><span class="pln">c</span><span class="pun">|}</span><span class="pln">       \hline       a </span><span class="pun">&</span><span class="pln"> b \\ \hline       c </span><span class="pun">&</span><span class="pln"> d\\       \hline     \end</span><span class="pun">{</span><span class="pln">tabular</span><span class="pun">}</span><span class="pln">   \end</span><span class="pun">{</span><span class="pln">center</span><span class="pun">}</span><span class="pln"> \end</span><span class="pun">{</span><span class="pln">document</span><span class="pun">}</span>

　　

注意观察有无\hline和有无\begin{center}的区别。注意观察\begin{tabular}后的lcr的区别，分别是left对齐，center对齐和right对齐。 

详细的Latex手册可以看下这篇博客

https://blog.csdn.net/gsww404/article/details/78684278?utm_medium=distribute.pc_relevant_download.none-task-blog-baidujs-1.nonecase&depth_1-utm_source=distribute.pc_relevant_download.none-task-blog-baidujs-1.nonecase

可以看一下一部分完成的工作展示、

\documentclass{article}
\usepackage{CJK}
\usepackage{ctex}
\usepackage{amsmath}
\begin{document}
\begin{CJK*}{GBK}{song}

作业一:\\

要使公式$\max\limits_{p_{1},...,p_{m}}-\sum\limits_{k=1}^{m}p_{k}logp_{k}$ 熵最大，根据最大熵原则可以引入拉格朗日因子$w_{0}$来表示对$\sum\limits_{k=1}^mp_{k}=1$ 的限制。有定义一个拉格朗日函数:
\begin{equation}
L(p,w)=\sum\limits_{i=1}^{m}p(y_{i})logp(y_{i})+w_{0}(\sum\limits_{i=1}^{m}p(y_{i})-1)
\end{equation}

根据拉格朗日对偶性，可以通过求解拉格朗日对偶最优化问题得到原始最优解的解，所以求解
\begin{equation}
\max\limits_{w}\min\limits_{p}L(p,w)
\end{equation}
首先可以先求解关于P的极小化问题，固定w0,求偏导数:
\begin{equation*}
\begin{aligned}
\partial L(p,w)/\partial p(y_{1}) &= 1+logp(y_{1}) + w0
\\
\partial L(p,w)/\partial p(y_{2}) &= 1+logp(y_{2}) + w0
\\
......
\\
\partial L(p,w)/\partial p(y_{m}) &= 1+logp(y_{m}) + w0
\\
\end{aligned}
\end{equation*}
令各偏导数为零，解得：
\begin{equation*}
\begin{aligned}
p(y_{1})=p_{2}=...=p(y_{m})=e^{-w0-1}
\end{aligned}
\end{equation*}
带入于是得
\begin{equation*}
\begin{aligned}
\min\limits_{p}L(p,w) = L(p_{w},w) = -me^{-w_{0}-1}-w_{0}
\end{aligned}
\end{equation*}
再求解$L(p_{w},w)$关于w得极大化问题:
\begin{equation*}
\begin{aligned}
\max\limits_{w}L(p,w) = L(p_{w},w) = -me^{-w_{0}-1}-w_{0}
\end{aligned}
\end{equation*}
分别对$L(P_{w},w)$对$w_{0}$的偏导数并令其为0，得到:$me^{-w_{0}-1}= 1$
所以$e^{-w_{0}-1} = 1/m$因此当每个$p_{i}=1/m$时取得最大熵,代入求得最大熵是$logm$


作业二:

因为
\begin{equation*}
\begin{aligned}
因为\int_{x}p_{data}(x)logD(x)\, dx + \int_{x}p_{G}(x)log(1-D(x))\, dx
\\
=\int_{x}[p_{data}(x)logD(x) + p_{G}(x)log(1-D(x))]\, dx
\end{aligned}
\end{equation*}
为简化表示，此时令$a = p_{data}(x)$, $b = logD(x)$, $c =p_{G}(x) $, $D = log(1-D(x))$
寻找一个x,这个最优化的D*使式子$aD + bD$最大即可，有
\begin{equation*}
\begin{aligned}
df(D)/dD &= a*1/D + b*1/(1-D)*(-1) = 0\\
a*1/D^{*} &= b*1/(1-D^{*})\\
a*(1-D^{*}) &= b*D^{*}\\
a - a*D^{*} &= b*D^{*}\\
D^{*} &= a/(a+b)\\
所以 D*(x) &= p_{data}(x)/p_{data}(x)+P_{G}(x)\\
\end{aligned}
\end{equation*}
为最优判别器
\end{CJK*}
\end{document}