Created
May 15, 2012 06:48
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ruhoh plugin to overload the redcarpet parser with mathjax tags
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# place mathjax.rb in _plugins directory of your blog | |
require 'redcarpet' | |
class HTMLwithAlbino < Redcarpet::Render::HTML | |
def block_code(code, language) | |
if language == 'mathjax' | |
"<script type=\"math/tex; mode=display\"> | |
#{code} | |
</script>" | |
else | |
"<pre><code class=\"#{language}\">#{code}</code></pre>" | |
end | |
end | |
def codespan(code) | |
if code[0] == "$" && code[-1] == "$" | |
code.gsub!(/^\$/,'') | |
code.gsub!(/\$$/,'') | |
"<script type=\"math/tex\">#{code}</script>" | |
else | |
"<code>#{code}</code>" | |
end | |
end | |
end | |
class Ruhoh | |
module Converter | |
module Markdown | |
def self.extensions | |
['.md', '.markdown'] | |
end | |
def self.convert(page) | |
markdown = Redcarpet::Markdown.new(HTMLwithAlbino.new(:with_toc_data => true), | |
:autolink => true, | |
:fenced_code_blocks => true | |
) | |
markdown.render(page.content) | |
end | |
end | |
end | |
end |
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--- | |
title: Numerical Differentiation | |
description: | |
layout: page | |
--- | |
## Derivative of a real function | |
The derivative of `$f(x)$` is | |
````mathjax | |
\begin{equation} | |
f'(x) = \lim_{h \rightarrow 0} \frac{f(x + h) - f(x)}{h} \label{eq:DerivativeDef} | |
\end{equation} | |
```` | |
suggest a naive approach to compute a numerical derivative: pick a small value `$h$` and apply \eqref{eq:DerivativeDef}. However, applied uncritically, this procedure is almost guaranteed to produce inaccurate results. | |
[Ridders](#Ridders) applied Romberg's method to improve the accuracy in the computation of the first and second derivatives of a real function. Using the Taylor expansion in the vicinity of `$x$`: | |
$$ | |
f'(x) \approx \frac{f(x + h) - f(x - h)}{2h} | |
$$ | |
with a truncation error of `$e_t \sim h^2 f^{(3)}$`. As a consequence, `$e_t$` decreases quadratically with decreasing `$h$`. |
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Is it possible to use only
$e^x$
(without backticks) to trigger MathJax?