A third example with MathJax activated

This StrapDown-flavored HTML page comes with MathJax enabled, simply because we asked the script to do so.

The last line of this page source (you can read it with "Ctrl+u" in Firefox) imports the script strapdown.min.js with this URL : "strapdown.min.js?src=example5&mathjax=y&theme=united&beacon=y".

This way, some options are available:

mathjax=y if you want to load MathJax, with $ ... $ being the default syntax for inline maths and $$ ... $$ for display,
theme=united or theme=cyborg if you want to load a specific theme (without having to specify it as the theme attribute of the main xmp tag containing your Markdown code),
beacon=y if you want to include an invisible GA Beacon image in your page,
pedantic=y if you want to force the use of the "pedantic" option for marked, the Markdown parser used by StrapDown.js (note: you probably don't want that, pedantic=false is usually better). Default is pedantic=false.
nonavbarfixed=y if you prefer the top navigation bar to not be fixed, but scroll as the rest of the page (new!). See example #8,
keepicon=y if you prefer StrapDown.js to keep the favicon included in your HTML document (new!). See example #9.
nonavbar=y if you prefer to not have any top navigation bar (new!). See example #10,

These examples are the same as the previous example 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 plugins.

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 third example with MathJax activated

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 third example with MathJax activated

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

An Identity of Ramanujan (obviously)

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 $|q|<1$}. 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

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

$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 $|q|<1$}.$