Markdown — Math Functions

Knowledge Base

Collection of the Math Examples

Refer to https://support.typora.io/Math/

https://gohugo.io/content-management/mathematics/

Base Math

Example:

$$
\begin{align*}
y = y(x,t) &= A e^{i\theta} \\
&= A (\cos \theta + i \sin \theta) \\
&= A (\cos(kx - \omega t) + i \sin(kx - \omega t)) \\
&= A\cos(kx - \omega t) + i A\sin(kx - \omega t)  \\
&= A\cos \Big(\frac{2\pi}{\lambda}x - \frac{2\pi v}{\lambda} t \Big) + i A\sin \Big(\frac{2\pi}{\lambda}x - \frac{2\pi v}{\lambda} t \Big)  \\
&= A\cos \frac{2\pi}{\lambda} (x - v t) + i A\sin \frac{2\pi}{\lambda} (x - v t)
\end{align*}
$$
$$ \begin{align*} y = y(x,t) &= A e^{i\theta} \\ &= A (\cos \theta + i \sin \theta) \\ &= A (\cos(kx - \omega t) + i \sin(kx - \omega t)) \\ &= A\cos(kx - \omega t) + i A\sin(kx - \omega t) \\ &= A\cos \Big(\frac{2\pi}{\lambda}x - \frac{2\pi v}{\lambda} t \Big) + i A\sin \Big(\frac{2\pi}{\lambda}x - \frac{2\pi v}{\lambda} t \Big) \\ &= A\cos \frac{2\pi}{\lambda} (x - v t) + i A\sin \frac{2\pi}{\lambda} (x - v t) \end{align*} $$

Chemistry

$$
$\ce{CH4 + 2 $\left( \ce{O2 + 79/21 N2} \right)$}$
$$
$$ $\ce{CH4 + 2 $\left( \ce{O2 + 79/21 N2} \right)$}$ $$

Cross Reference

$$
x+1\over\sqrt{1-x^2}\label{ref1}\tag{1}
$$
$$ x+1\over\sqrt{1-x^2}\label{ref1}\tag{1} $$

Line Break

Line break within math mode.

$$ 
x + y = 2\\x - y = 4 
$$
$$ x + y = 2\\x - y = 4 $$

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