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수학 표현 식

방정식 표현하기1

\begin{align} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{align}

방정식 표현하기2

\begin{equation*} \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1})^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \end{equation*}

행렬식 표현하기

\begin{equation*} \mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix} \end{equation*}

확률관련 수식

\begin{equation*} P(E) = {n \choose k} p ^k (1-p)^{ n-k} \end{equation*}

무한분수 표현1

\begin{equation*} \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } } \end{equation*}

등식 표현

\begin{equation*} 1 + \ frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod_ {j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j3})}, \quad\quad \text{for $|q|<1$}, \end{equation*}

맥스웰 방정식

\begin{align} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \\times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}} {\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{align}

문장속의 수식 표현

This exoression $\sqrt{3x-1}+(1+x)^2$ is an example of a TeX inline equation in a Markdown-formatted sentence.

그외 표현들

$$\begin{eqnarray} x' &=& &x \sin\phi &+& z \cos\phi \\ z' &=& - &x \cos\phi &+& z \sin\phi \\ \end{eqnarray}$$$$ x=4 $$