A second example with MathJax activated (and the paper theme)

To know how to include MathJax in a StrapDown-flavored HTML page, you can read this example 3. To discover an even nicer way to import MathJax, read the last example.

These examples are directly imported from the samples from the mathjax.org website.

The following equations are included in the HTML source code as pure LaTeX code.

$\left\{\begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned}\right.$

The previous equation corresponds to the following code, inserted verbatim in the Markdown part of this page (ie. after the opening xmp tag and before its closing):
$$\left\\\{\begin{aligned}
\dot{x} & = \sigma(y-x) \\\\
\dot{y} & = \rho x - y - xz \\\\
\dot{z} & = -\beta z + xy
\end{aligned}\right. $$

The Cauchy-Schwarz Inequality (in $\mathbb{R}^n$ )

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

The previous equation corresponds to the following code, inserted verbatim in the Markdown part of this page:
$$ \left( \sum\_{k=1}^n a\_k b\_k \right)^2 \leq \left( \sum\_{k=1}^n a\_k^2 \right) \left( \sum\_{k=1}^n b\_k^2 \right) $$

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

The previous equation corresponds to the following code, inserted verbatim in the Markdown part of this page:

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

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

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

The previous equation corresponds to the following code, inserted verbatim in the Markdown part of this page:
$$P(E) = {n \choose k} p^k (1-p)^{n-k} $$

An Identity of Ramanujan (obviously)

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

The previous equation corresponds to the following code, inserted verbatim in the Markdown part of this page:
$$ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
{1+\frac{e^{-8\pi}} {1+\ldots} } } } $$

$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 $|q|<1$}.$

The previous equation corresponds to the following code, inserted verbatim in the Markdown part of this page:
$$  1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
\prod\_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
\quad\quad \text{for $|q|&lt;1$}. $$

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

The previous equation corresponds to the following code, inserted verbatim in the Markdown part of this page:

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

As you can see, math environment (like aligned) are supported by MathJax, even with the default configuration and no external plugin.

Inline equations are also supported.

Finally, while display equations look good for a page of samples, the ability to mix math and text in a paragraph is also important. This expression $\sqrt{3x-1}+(1+x)^2$ is an example of an inline equation (inserted with the code $\sqrt{3x-1}+(1+x)^2$ ). As you see, MathJax equations can be used this way as well, without unduly disturbing the spacing between lines.

End of the examples

That's all for today!

A second example with MathJax activated (and the paper theme)

The Lorenz Equations

$\left\{\begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned}\right.$

The Cauchy-Schwarz Inequality (in $\mathbb{R}^n$ )

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

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 (obviously)

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

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 \text{for $|q|<1$}.$

Maxwell's Equations

Inline equations are also supported.

End of the examples

A second example with MathJax activated (and the paper theme)

The Lorenz Equations

{˙x=σ(y−x)˙y=ρx−y−xz˙z=−βz+xy\left\{\begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned}\right.

The Cauchy-Schwarz Inequality (in Rn\mathbb{R}^n)

(n∑k=1akbk)2≤(n∑k=1a2k)(n∑k=1b2k) \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

V1×V2=|ijk∂X∂u∂Y∂u0∂X∂v∂Y∂v0|\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 kk heads when flipping nn coins is

P(E)=(nk)pk(1−p)n−kP(E) = {n \choose k} p^k (1-p)^{n-k}

An Identity of Ramanujan (obviously)

1(√ϕ√5−ϕ)e25π=1+e−2π1+e−4π1+e−6π1+e−8π1+… \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+q2(1−q)+q6(1−q)(1−q2)+⋯=∞∏j=01(1−q5j+2)(1−q5j+3),for |q|<1. 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 $|q|<1$}.

Maxwell's Equations

Inline equations are also supported.

End of the examples

$\left\{\begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned}\right.$

The Cauchy-Schwarz Inequality (in $\mathbb{R}^n$ )

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

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

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

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

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

$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 $|q|<1$}.$