User:Jmkim dot com/TeX Samples


 * TeX Samples
 * TeX 샘플

nowiki Test
$$E=mc^2$$

$$E=mc^2$$

Inequality Sign Test
$$1<2$$

$$2>1$$

$$1\lt 2$$

$$2\gt 1$$

$$2\geq 1$$

Inequality Sign Test 2
$$ab$$

$$a > b$$

$$f(x)=1 $$

UTF-8 Test
$$전압 = 전류 \times 저항$$

$$\mbox{전압} = \mbox{전류} \times \mbox{저항}$$

$$저항 = \frac{전압}{전류}$$

$$\mbox{저항} = \frac{\mbox{전압}}{\mbox{전류}}$$

$$n$$개의 동전을 던져 앞면 $$k$$가 나올 확률 $$P(E)$$는?

$$償還までの合計利回り =\left(1+\frac{期間利率}{100}\right)^{期間}$$

$$\mbox{償還までの合計利回り} =\left(1+\frac{\mbox{期間利率}}{100}\right)^{\mbox{期間}}$$

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

The Cauchy-Schwarz Inequality
$$\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$$

A Cross Product Formula
$$\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix}$$

The probability of getting k heads when flipping n coins is
$$P(E)  = {n \choose k} p^k (1-p)^{ n-k}$$

An Identity of Ramanujan
$$\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } }$$

A Rogers-Ramanujan Identity
$$1 + \frac{q^2}{(1-q)} + \frac{q^6}{(1-q)(1-q^2)} + \cdots = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad for\,|q|<1.$$

Maxwell’s Equations
$$\begin{align} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\  \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{align}$$

같이 보기

 * TeX

참고 자료

 * https://www.mediawiki.org/wiki/Extension:SimpleMathJax
 * http://www.mathjax.org/demos/tex-samples/