# 增加了markdown写数学公式的功能

When $a \ne 0$, there are two solutions to $ax^2 + bx + c = 0$and they are

$$x = {-b \pm \sqrt{b%^2-4ac} \over 2a}.$$

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

## 朴素贝叶斯公式:

$$P(w_1 , w_2) = P(w_2|w_1) * P(w_1)$$

## Double angle formula for Cosines

$$\cos(θ+φ)=\cos(θ)\cos(φ)−\sin(θ)\sin(φ)$$

## Cauchy's Integral Formula

$$f(a) = \frac{1}{2\pi i} \oint\frac{f(z)}{z-a}dz$$

## Curl of a Vector Field

$$\vec{\nabla} \times \vec{F} = \left( \frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z} \right) \mathbf{i} + \left( \frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} \right) \mathbf{j} + \left( \frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} \right) \mathbf{k}$$

## Gauss' Divergence Theorem

$$\int_D ({\nabla\cdot} F)dV=\int_{\partial D} F\cdot ndS$$

## Definition of Christoffel Symbols

$$(\nabla_X Y)^k = X^i (\nabla_i Y)^k = X^i \left( \frac{\partial Y^k}{\partial x^i} + \Gamma_{im}^k Y^m \right)$$

## Standard Deviation

$$\sigma = \sqrt{ \frac{1}{N} \sum_{i=1}^N (x_i -\mu)^2}$$

2018-12-19 15:42