a1ddf43baa
- [X] Fix a few English typos in examples, - [X] Shorter list of examples for index.html, - Add a 'keepicon=y' option to ask strapdown.js to not replace the favicon while being loaded, - For the http://lbesson.bitbucket.org/md/example9.html page, add a favicon.ico file (in ..)
116 lines
6.2 KiB
HTML
116 lines
6.2 KiB
HTML
<!DOCTYPE html><html><head><meta charset="utf-8"/><title>A second demo of MathJax with StrapDown.js</title></head><body><xmp theme="paper">
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<ul class="pager">
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<li class="previous"><a href="example3.html">← Previous example</a></li>
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<li><a href="index.html">Index</a></li>
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<li class="next"><a href="example5.html">Next example →</a></li>
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</ul>
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# A second example with [MathJax](http://www.mathjax.org/) activated (and the *paper* theme)
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> To know how to include MathJax in a *StrapDown*-flavored HTML page, you can read this [example 3](example3.html).
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To discover an even nicer way to import MathJax, read [the last example](example5.html).
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> These examples are directly imported from [the samples from the mathjax.org website](http://www.mathjax.org/demos/tex-samples/).
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> The following equations are included in the HTML source code as **pure LaTeX code**.
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***
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### The [Lorenz Equations](https://en.wikipedia.org/wiki/Lorenz_system#Overview)
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### $$\left\\\{\begin{aligned} \dot{x} & = \sigma(y-x) \\\\ \dot{y} & = \rho x - y - xz \\\\ \dot{z} & = -\beta z + xy \end{aligned}\right. $$
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> 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):
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```latex
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$$\left\\\{\begin{aligned}
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\dot{x} & = \sigma(y-x) \\\\
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\dot{y} & = \rho x - y - xz \\\\
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\dot{z} & = -\beta z + xy
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\end{aligned}\right. $$
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```
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### The [Cauchy-Schwarz Inequality](https://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality#Rn) (in $\mathbb{R}^n$)
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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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> The previous equation corresponds to the following code, inserted *verbatim* in the Markdown part of this page:
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```latex
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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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```
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### A [Cross Product](https://en.wikipedia.org/wiki/Cross_product#Coordinate_notation) 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 previous equation corresponds to the following code, inserted *verbatim* in the Markdown part of this page:
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```latex
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$$\mathbf{V}\_1 \times \mathbf{V}\_2 = \begin{vmatrix}
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\mathbf{i} & \mathbf{j} & \mathbf{k} \\\\
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\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\\\
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\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0
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\end{vmatrix} $$
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```
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### The probability of [getting $k$ heads when flipping $n$ coins](https://en.wikipedia.org/wiki/Bernoulli_process#Binomial_distribution) is
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### $$P(E) = {n \choose k} p^k (1-p)^{n-k} $$
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> The previous equation corresponds to the following code, inserted *verbatim* in the Markdown part of this page:
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```latex
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$$P(E) = {n \choose k} p^k (1-p)^{n-k} $$
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```
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### An Identity of Ramanujan (obviously)
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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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> The previous equation corresponds to the following code, inserted *verbatim* in the Markdown part of this page:
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```latex
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$$ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
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1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
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{1+\frac{e^{-8\pi}} {1+\ldots} } } } $$
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```
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### A [Rogers-Ramanujan Identity](https://en.wikipedia.org/wiki/Rogers%E2%80%93Ramanujan_identities)
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### $$ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod\_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for $|q|<1$}. $$
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> The previous equation corresponds to the following code, inserted *verbatim* in the Markdown part of this page:
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```latex
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$$ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
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\prod\_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
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\quad\quad \text{for $|q|<1$}. $$
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```
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### [Maxwell's Equations](https://en.wikipedia.org/wiki/Maxwell%27s_equations)
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### $$ \left\\\{\begin{aligned} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\\\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\\\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\\\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}\right. $$
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> The previous equation corresponds to the following code, inserted *verbatim* in the Markdown part of this page:
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```latex
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$$ \left\\\{\begin{aligned}
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\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\\\
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\nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\\\
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\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\\\
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\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}\right.
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$$
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```
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As you can see, math environment (like ``aligned``) are supported by MathJax, even with the default configuration and no external plugin.
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****
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### Inline equations are also supported.
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Finally, while **display equations** look good for a page of samples, the ability to mix math and text in a paragraph is also important.
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This expression $\sqrt{3x-1}+(1+x)^2$ is an example of an **inline equation** (inserted with the code ``$\sqrt{3x-1}+(1+x)^2$``).
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As you see, MathJax equations can be used this way as well, without unduly disturbing the spacing between lines.
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### End of the examples
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That's all for today!
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---
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<ul class="pager">
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<li class="previous"><a href="example3.html">← Previous example</a></li>
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<li><a href="index.html">Index</a></li>
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<li class="next"><a href="example5.html">Next example →</a></li>
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</ul>
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</xmp>
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<script type="text/x-mathjax-config">MathJax.Hub.Config({ tex2jax: { inlineMath: [['$','$']], displayMath: [['$$', '$$']], processEscapes: true } });</script>
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<script type="text/javascript" src="//cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
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<script type="text/javascript" src="//lbesson.bitbucket.org/md/strapdown.min.js?src=example4"></script>
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</body></html>
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