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Nikhil Kumar

A stylish blog on my code

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Changelog:

Happy Pie Day

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:

$$e^{\pi i} = -1$$
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$$ e^{\pi i} = -1 $$

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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$$f(x) = f(a) + f^{\prime}(a)(x-a) + \frac{f^{\prime \prime}(a)}{2!} (x-a)^2...\frac{f^{n}(a)}{n!} (x-a)^n$$