- TeX Samples
- TeX 샘플
1 한글 테스트
[math]\displaystyle{ 전압 = 전류 \times 저항 }[/math]
2 한글 테스트 2
[math]\displaystyle{ 저항 = \frac{전압}{전류} }[/math]
3 The Lorenz Equations
[math]\displaystyle{ \begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned} }[/math]
4 The Cauchy-Schwarz Inequality
[math]\displaystyle{ \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) }[/math]
5 A Cross Product Formula
[math]\displaystyle{ \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} }[/math]
6 The probability of getting [math]\displaystyle{ k }[/math] heads when flipping [math]\displaystyle{ n }[/math] coins is
[math]\displaystyle{ P(E) = {n \choose k} p^k (1-p)^{ n-k} }[/math]
7 An Identity of Ramanujan
[math]\displaystyle{ \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} } } } }[/math]
8 A Rogers-Ramanujan Identity
[math]\displaystyle{ 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 \text{for $|q|<1$}. }[/math]
9 Maxwell's Equations
[math]\displaystyle{ \begin{aligned} \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{aligned} }[/math]
10 참고 자료
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