Mathematical Notations with Mathjax

Let’s try some mathematical notations with MathJax.

Functions

Polynomial Function

$ f(x) = x^2 $

$ f(x) = x^2 $

Definition of e

$ \lim_{n\to \infty}(1+\frac{1}{n})^n = e $

$ \lim_{n\to \infty}(1+\frac{1}{n})^n = e $

Linear Algebra

Singular Value Decomposition (SVD)

$ A = U \Sigma V^T $

$ A = U \Sigma V^T $

Calculus

Chain Rule

$ \frac{dz}{dt} = \frac{\partial f}{\partial x} \frac{dx}{dt} + \frac{\partial f}{\partial y} \frac{dy}{dt} $

$ \frac{dz}{dt} = \frac{\partial f}{\partial x} \frac{dx}{dt} + \frac{\partial f}{\partial y} \frac{dy}{dt} $

Change to Polar Coordinates

$ \iint\limits_{D} f(x,y) \,dA = \int_{\alpha}^{\beta} \int_{h_1(\theta)}^{h_2(\theta)} f(rcos\theta, rsin\theta)r\,dr\,d\theta $

$ \iint\limits_{D} f(x,y) \,dA = \int_{\alpha}^{\beta} \int_{h_1(\theta)}^{h_2(\theta)} f(rcos\theta, rsin\theta)r\,dr\,d\theta $