S H I N E: May 2020

Friday, May 29, 2020

Write multi-line equation in the blogger

After we involved the mathjax in the blogger (https://qinglanseyu.blogspot.com/2018/09/how-to-insert-formula-in-google-blogger.html), we can write multiple line equations very easy. We just need to add "\\" at the end of every single equation.

Example:

It will shown,

\[ a + b = c +d \\ = d + f .\]

Integration in the spherical coordinate

\[ d^3r = r^2 dr \sin\theta d\theta d\phi \]

Since $d\cos(\theta)=-\sin(\theta)d\theta$,

\[ d^3r = -r^2 dr d\cos(\theta) d\phi ,\]

let $\mu = \cos(\theta)$,

\[ \int \int \int_0^{\pi} d^3r = \int \int \int_0^{\pi} -r^2 dr d\cos(\theta) d\phi \\ = \int \int \int_{\cos(0)}^{\cos(2\pi)} -r^2 dr d\mu d\phi \\ =\int \int \int_{\cos(0)}^{\cos(2\pi)} -r^2 dr d\mu d\phi \\ = \int \int \int_{\cos(2\pi)}^{\cos(0)} r^2 dr d\mu d\phi \\ = \int \int \int_{-1}^{1} r^2 dr d\mu d\phi \]