reveal.js - Math Plugin

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reveal.js Math Plugin

A thin wrapper for MathJax

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The Lorenz Equations

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

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The Cauchy-Schwarz Inequality

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

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A Cross Product Formula

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

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The probability of getting $k$ heads when flipping $n$ coins is

- - \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \] -

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An Identity of Ramanujan

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

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A Rogers-Ramanujan Identity

- - \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = - \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\] -

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Maxwell’s Equations

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

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The Lorenz Equations

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

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The Cauchy-Schwarz Inequality

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- \[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \] -

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A Cross Product Formula

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

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The probability of getting $k$ heads when flipping $n$ coins is

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- \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \] -

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An Identity of Ramanujan

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

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A Rogers-Ramanujan Identity

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- \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = - \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\] -

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Maxwell’s Equations

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

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