Typora——数学公式
1. 分数\平方\下标
| 算式 |
markdown |
| \(\frac{7x_1}{1+y_{3}^2}\) |
\frac{7x_1}{1+y_{3}^2} |
2. 省略号
| 省略号 |
markdown |
| \(\cdots\) |
\cdots |
3. 根号
| 根号 |
markdown |
| \(\sqrt{2},\sqrt{n}\) |
\sqrt{2},\sqrt |
4. 矢量\点乘
| 矢量 |
markdown |
| \(\vec{A} \cdot \vec{B}\) |
\vec{A} \cdot \vec |
5. 积分
| 积分 |
markdown |
| \(\int ^{2}_{4} x^2 {\rm d1}\) |
\int ^{2}_{4} x^2 |
6. 极限
| 极限 |
markdown |
| \(\lim_{n\rightarrow+\infty}n\) |
\lim_{n\rightarrow+\infty}n |
7. 累加|分数
| 累加 |
markdown |
| \(\sum\frac{1}{i^2}\) |
\sum\frac{1} |
8. 累乘
| 累乘 |
markdown |
| \(\prod\frac{1}{i^2}\) |
\prod\frac{1} |
9. 希腊字母
| 大写 |
markdown |
小写 |
markdown |
| A |
A |
\(\alpha\) |
\alpha |
| B |
B |
\(\beta\) |
\beta |
| \(\Gamma\) |
\Gamma |
\(\gamma\) |
\gamma |
| \(\Delta\) |
\Delta |
\(\delta\) |
\delta |
| E |
E |
\(\epsilon\) |
\epsilon |
|
|
\(\varepsilon\) |
\varepsilon |
| Z |
Z |
\(\zeta\) |
\zeta |
| H |
H |
\(\eta\) |
\eta |
| \(\Theta\) |
\Theta |
\(\theta\) |
\theta |
| I |
I |
\(\iota\) |
\iota |
| K |
K |
\(\kappa\) |
\kappa |
| \(\Lambda\) |
\Lambda |
\(\lambda\) |
\lambda |
| N |
N |
\(\nu\) |
\nu |
| \(\Xi\) |
\Xi |
\(\xi\) |
\xi |
| O |
O |
\(\omicron\) |
\omicron |
| \(\Pi\) |
\Pi |
\(\pi\) |
\pi |
| P |
\P |
\(\rho\) |
\rho |
| \(\Sigma\) |
\Sigma |
\(\sigma\) |
\sigma |
| T |
T |
\(\tau\) |
\tau |
| \(\Phi\) |
\Phi |
\(\phi\) |
\phi |
|
|
\(\varphi\) |
\varphi |
| X |
X |
\(\chi\) |
\chi |
| \(\Psi\) |
\Psi |
\(\psi\) |
\psi |
| \(\Omega\) |
\Omega |
\(\omega\) |
\omega |
10. 三角函数
| 三角函数 |
markdown |
| \(\sin \\ \cos \\ \tan \\\tanh\) |
\sin \ \cos \ \tan \\tanh |
11. 对数函数
| 对数函数 |
markdown |
| \(\ln12\) |
\ln15 |
| \(\log_2 10\) |
\log_2 10 |
| \(\lg7\) |
\lg7 |
12. 关系运算符
| 运算符 |
markdown |
| $\pm $ |
\ |
| \(\times\) |
\times |
| \(\div\) |
\div |
| $ \sum$ |
\sum |
| $ \prod$ |
\prod |
| $ \neq$ |
\neq |
| $ \leq$ |
\leq |
| $ \geq$ |
\geq |
13. 综合
\frac{d}{dx}e^{ax} = ae^{ex} \sum_{i=1}^{n}(X_i-\overline{X})^2
\[\frac{d}{dx}e^{ax} = ae^{ex} \sum_{i=1}^{n}(X_i-\overline{X})^2
\]
14. 添加
\[\sum\beta_{测} = 2519^{°}58^{′}29^{″} \space\space\space\space\space
\sum\beta_{理} = 2520^{°}00^{′}00^{″} \\
f_{\beta允} = \pm40^{″}\sqrt{n} = \pm160^{″} \space\space\space\space\space
f_{\beta} = \sum\beta_{理} - \sum\beta_{测} = 91^{″} \le 160^{″} \\
f_y = \sum \Delta y_测 = 0.113m \space\space\space\space\space
f_x = \sum \Delta x_测 = -0.024m \\
全长闭合差\space f = \sqrt{f_x^2 + f_y^2} = 0.1155m \\
允许相对闭合差 \space k = \frac{1}{6000} \\
全长相对闭合差 k^{′} = \frac{1}{\sum{D}/{f}} \le \frac{1}{6000}
\]
\[\sum\beta_{测} = 539^{°}59^{′}13^{″} \space\space\space\space\space
\sum\beta_{理} = 540^{°}00^{′}00^{″} \\
f_{\beta允} = \pm40^{″}\sqrt{n} = \pm89.4^{″} \space\space\space\space\space
f_{\beta} = \sum\beta_{理} - \sum\beta_{测} = -47^{″} \le f_{\beta允} \\
f_x = \sum \Delta x_测 = -0.0120m \space\space\space\space\space
f_y = \sum \Delta y_测 = 0.0250m \\
全长闭合差\space f = \sqrt{f_x^2 + f_y^2} = 0.0277m \\
允许相对闭合差 \space k = \frac{1}{6000} \\
全长相对闭合差 k^{′} = \frac{1}{\sum{D}/{f}} \le \frac{1}{6000}
\]
15. 多行公式
\[方法一：
f(x)=\left\{
\begin{aligned}
x & = \cos(t) \\
y & = \sin(t) \\
z & = \frac xy
\end{aligned}
\right.
\\
方法二：
F^{HLLC}=\left\{
\begin{array}{rcl}
F_L & & {0 < S_L}\\
F^*_L & & {S_L \leq 0 < S_M}\\
F^*_R & & {S_M \leq 0 < S_R}\\
F_R & & {S_R \leq 0}
\end{array} \right.
\\
方法三:
f(x)=
\begin{cases}
0& \text{x=0}\\
1& \text{x!=0}
\end{cases}
\]
