美妙的数学


一切皆是映射(Mapping),映射即流(Stream),流即函数: $y=f(x)$
(By 一个会写诗的程序员)

Latex语法参考

公式 Latex代码
$\sqrt x$ $\sqrt(x)$
$\sqrt[3]{x}$ $\sqrt[3]{x}$
$e^{x^2} \neq {e^x}^2$ $e^{x^2} \neq {e^x}^2$
$a^{3}_{ij}$ $a^{3}_{ij}$
$e^{-\alpha t}$ $e^{-\alpha t}$
$a\ b$ $a\ b$
$a\quad b$ $a\quad b$
$ \geq$ $ \geq$
$\leq $ $\leq $
$\frac{1}{2} $ $\frac{1}{2} $
$x_{2}$ $x_{2}$
$x^{2}$ $x^{2}$
$a \ne 0$ $a \ne 0$
$ax^2 + bx + c = 0$ $ax^2 + bx + c = 0$
$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$ $x = {-b \pm \sqrt{b^2-4ac} \over 2a}$
$\overline{m+n}$ $\overline{m+n}$
$\underline{m+n}$ $\underline{m+n}$
$\underbrace{a + b + \cdots + z}_{26}$ $\underbrace{a + b + \cdots + z}_{26}$
$\overrightarrow{AB}$ $\overrightarrow{AB}$
$\vec{c}$ $\vec{c}$
$\frac{x^2}{k+1}$ $\frac{x^2}{k+1}$
$(x-y)^2\equiv(-x+y)^2\equiv x^2-2xy+y^2$ $(x-y)^2\equiv(-x+y)^2\equiv x^2-2xy+y^2$
$x'$ $x'$
$\dot{x} \ \ddot{x}$ $\dot{x} \ \ddot{x}$
$\sum_{k=1}^N k^2$ $\sum_{k=1}^N k^2$
$\prod_{i=1}^N x_i$ $\prod_{i=1}^N x_i$
$\lim_{n \to \infty}x_n$ $\lim_{n \to \infty}x_n$
$\int_{-N}^{N} e^x\, dx$ $\int_{-N}^{N} e^x\, dx$
$\iiint_{E}^{V} \, dx\,dy\,dz$ $\iiint_{E}^{V} \, dx\,dy\,dz$
$\oint_{C} x^3\, dx + 4y^2\, dy$ $\oint_{C} x^3\, dx + 4y^2\, dy$
$\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} =a$ $\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} =a$
$\dbinom{n}{r}=\binom{n}{n-r}=C^n_r=C^n_{n-r}$ $\dbinom{n}{r}=\binom{n}{n-r}=C^n_r=C^n_{n-r}$
$\begin{matrix} x & y \\ z & v \end{matrix}$ $\begin{matrix} x & y \\ z & v \end{matrix}$
$\begin{vmatrix} x & y \\ z & v \end{vmatrix}$ $\begin{vmatrix} x & y \\ z & v \end{vmatrix}$
$\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}$ $\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}$
$\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}$ $\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}$
$\begin{pmatrix} x & y \\ z & v \end{pmatrix}$ $\begin{pmatrix} x & y \\ z & v \end{pmatrix}$
$f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases}$ $f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases}$
$\begin{align} f(x) & = (m+n)^2 \\ & = m^2+2mn+n^2 \\ \end{align}$ $\begin{align} f(x) & = (m+n)^2 \\ & = m^2+2mn+n^2 \\ \end{align}$
$\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}$ $\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}$
$f(x) \,\! = \sum_{n=0}^\infty a_n x^n = a_0+a_1x+a_2x^2+\cdots$ $f(x) \,\! = \sum_{n=0}^\infty a_n x^n = a_0+a_1x+a_2x^2+\cdots$
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