# LaTeX Tutorial
###### tags: `Tutorial`
###### author: `Jia-Wei, Liao`

## 註冊 Overleaf
* [Overleaf 網站](https://www.overleaf.com/)

## 基本模板

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amssymb, amsthm}  %AMS數學套件%
\begin{document}

%%%%%%%%%%%%%%%%%%%% 可以開始打字 %%%%%%%%%%%%%%%%%%%%

This is a example.

\end{document}

#### Remark
% 為 LaTeX 的註解，不會進行編譯

## 基本數學指令
通常一般文字會打 x (正體)，而數學變數會打成 $x$ (斜體)
數學模式要在指令的前後加上 `$`，指令前面要加 `\`
* **希臘字母:** `$\alpha$` $\to$ $\alpha$
* **三角函數:** `$\sin x$` $\to$ $\sin x$
* **次方:** `$a^b$` $\to$ $a^b$
* **下標:** `$a_n$` $\to$ $a_n$
* **分數:** `$\frac{1}{2}$` $\to$ $\frac{1}{2}$
* **根號:** `$\sqrt{2}$` $\to$ $\sqrt{2}$; `$\sqrt[3]{2}$` $\to$ $\sqrt[3]{2}$
* **極限:** `$\lim$` $\to \lim$
* **累積:** `$\sum$` $\to$ $\sum$
* **積分:** `$\int$` $\to$ $\int$
* **因為:** `$\because$` $\to$ $\because$
* **所以:** `$\therefore$` $\to$ $\therefore$
* **箭頭:** `$\to$` $\to$ $\to$
* **小於等於:** `\leq` $\to$ $\leq$
* **大於等於:** `\geq` $\to$ $\geq$

#### Remark
* 更多指令請參考 [LaTeX符號指令](https://drive.google.com/file/d/1eUTzNATdPz7Xm2dK6HF-oqRfgBsd5EaP/view)
* 覺得數學式子太小可以用 `\displaystyle` 來調整

#### Exercise
* $ax^2+bx+c$
:::spoiler 顯示答案
`$ax^2+bx+c$`
:::

* $x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$
:::spoiler 顯示答案
`$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$`
:::

* $\log_a(x+y)= \log_ax+\log_ay$
:::spoiler 顯示答案
`$\log_a(x+y)= \log_ax+\log_ay$`
:::

* $\int_a^b f(x) dx=F(b)-F(a)$
:::spoiler 顯示答案
`$\int_a^b f(x) dx=F(b)-F(a)$`
:::

* $\displaystyle \lim_{x \to a} f(x) = f(a)$
:::spoiler 顯示答案
`$\displaystyle \lim_{x \to a} f(x) = f(a)$`
:::

* $\displaystyle \sum_{k=1}^n k^2=\frac{n(n+1)(2n+1)}{6}$
:::spoiler 顯示答案
`$\displaystyle \sum_{k=1}^n k^2=\frac{n(n+1)(2n+1)}{6}$`
:::

* $|a+b| \leq |a|+|b|$
:::spoiler 顯示答案
`$|a+b| \leq |a|+|b|$`
:::

## 空格
* `\,`
* `\quad`
* `\hspace{1cm}`
* `\noindent` : 開頭不空兩格

## 程式碼

\usepackage{listings}
\usepackage{xcolor}
\usepackage{color}
\definecolor{dkgreen}{rgb}{0,0.6,0}
\definecolor{gray}{rgb}{0.5,0.5,0.5}
\definecolor{mauve}{rgb}{0.58,0,0.82}

\lstset{frame=tb,
  language=MATLAB,
  aboveskip=3mm,
  belowskip=3mm,
  showstringspaces=false,
  columns=flexible,
  basicstyle={\small\ttfamily},
  numbers=left,
  numberstyle=\tiny\color{gray},
  keywordstyle=\color{blue},
  commentstyle=\color{dkgreen},
  stringstyle=\color{mauve},
  breaklines=true,
  breakatwhitespace=true,
  tabsize=3,
  backgroundcolor=\color{gray!2}
}

\begin{lstlisting}
   ## your code
\end{lstlisting}

## Beamer基本模板
- [官網基本模板](https://www.overleaf.com/learn/latex/Beamer)

\documentclass{beamer}
\title{Sample title}
\author{Anonymous}
\institute{Overleaf}
\date{2021}

\begin{document}

\frame{\titlepage}

\begin{frame}
\frametitle{Sample frame title}
This is some text in the first frame.
This is some text in the first frame.
This is some text in the first frame.
\end{frame}

\end{document}

## 更改主題

\usetheme{Madrid}

## 特殊指令

| 指令 | 編譯 |
| -------- | -------- |
| `0 \stackrel{a}{\longrightarrow} 1` | $0\stackrel{a}{\longrightarrow}1$ |
|`{n \choose i}` | ${n \choose i}$ |
|`{{\text {iid} \atop \sim} \atop}`| ${{\text {iid} \atop \sim}\atop}$|