In honor of Pie day I decided to learn how to incorporate a math typeset onto
Html. The mathjax package makes this easy to do.
Setting up the html
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<script type= "text/x-mathjax-config" >
MathJax . Hub . Config ({ tex2jax : { inlineMath : [[ ' $ ' , ' $ ' ], [ ' \\ ( ' , ' \\ ) ' ]]}});
</script>
<script type= "text/javascript"
src= "https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" >
</script>
Usage
You can now insert LaTeX equations in html by inserting them in the middle of two $$ for an equation on a new line and two $ for an equation on the same line..
Some cool $\pi$ stuff:
Euler's identity:
$$e^{\pi i} = -1$$
Heisenberg's uncertainty principle:
$$\Delta x \Delta p \geq \frac{h}{4\pi}$$
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$$ \Delta x \Delta p \geq \frac { h }{ 4 \pi }$$
Schrödinger Equation
$$\frac{ih}{2\pi} \frac{\partial}{\partial t} \Psi (x,t) = - \frac{h}{4\pi m}
\bigtriangledown^2 \Psi (x,t) + V(x) \Psi (x,t) $$
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$$ \frac { ih }{ 2 \pi } \frac { \partial }{ \partial t } \Psi ( x,t ) = - \frac { h }{ 4 \pi m }
\bigtriangledown ^ 2 \Psi ( x,t ) + V ( x ) \Psi ( x,t ) $$
Integral approximation:
$$\int^\infty_{-\infty} \int^\infty_t e^{-t^2 - \frac{1}{2}x^2 + xt} \,dx\,dt = \pi $$
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$$ \int ^ \infty _{ - \infty } \int ^ \infty _ t e ^{ - t ^ 2 - \frac { 1 }{ 2 } x ^ 2 + xt } \, dx \, dt = \pi $$
Infinite Series approximation:
$$\sum_{n=1}^\infty \frac{3^n -1}{4^n} \zeta (n + 1) = \pi $$
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$$ \sum _{ n = 1 }^ \infty \frac { 3 ^ n - 1 }{ 4 ^ n } \zeta ( n + 1 ) = \pi $$
Some cool engineering equations:
Normal Distribution:
$$\Phi (x) = \frac{1}{\sqrt{2\pi\sigma}} e^{\frac{(x-\mu)^2}{2 \sigma^2}}$$
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$$ \Phi ( x ) = \frac { 1 }{ \sqrt { 2 \pi\sigma }} e ^{ \frac { ( x - \mu ) ^ 2 }{ 2 \sigma ^ 2 }}$$
Fourier Transform
$$\int^\infty_{-\infty} f(x)e^{-2\pi i x \zeta} \,dx = f(\zeta) $$
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$$ \int ^ \infty _{ - \infty } f ( x ) e ^{ - 2 \pi i x \zeta } \, dx = f ( \zeta ) $$
Taylor Series
$$f(x) = f(a) + f^{\prime}(a)(x-a) + \frac{f^{\prime \prime}(a)}{2!} (x-a)^2...\frac{f^{n}(a)}{n!} (x-a)^n$$
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$$ f ( x ) = f ( a ) + f ^{ \prime } ( a )( x - a ) + \frac { f ^{ \prime \prime } ( a ) }{ 2 ! } ( x - a ) ^ 2 ... \frac { f ^{ n } ( a ) }{ n ! } ( x - a ) ^ n $$
