Math with KaTeX

This blog supports mathematical notation using KaTeX. You can use LaTeX syntax to render math equations.

Inline Math

You can write inline math by wrapping your equation in single dollar signs $.

For example, $E = mc^2$ renders as $E = mc^2$.

Block Math

For larger equations that should be displayed on their own line, use double dollar signs $$.

$$
\int_{0}^{\infty} x^2 e^{-x} \, dx = 2!
$$

Renders as:

Common Notations Reference

Here is a quick reference for the most commonly used mathematical notations.

Roots and Exponents

Trigonometry

Logarithms and Calculus

Operators and Logic

Boolean Logic

Example:

$(P \land Q) \implies R$ $\rightarrow$ $(P \land Q) \implies R$

Functions

You can define functions using standard algebraic notation.

Simple Function:

$f(x) = \sin(x) + \cos(x)$ $\rightarrow$ $f(x) = \sin(x) + \cos(x)$

Piecewise Function:

$$
f(x) = \begin{cases}
  x^2 & \text{if } x > 0 \\
  -x & \text{if } x \le 0
\end{cases}
$$

Derivatives

Express derivatives using prime notation or Leibniz notation.

Prime Notation:

$f'(x) = 2x + 1$ $\rightarrow$ $f'(x) = 2x + 1$

Leibniz Notation:

$\frac{dy}{dx} = 3x^2$ $\rightarrow$ $\frac{dy}{dx} = 3x^2$

Limit Definition:

$$
\frac{df}{dx} = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}
$$

Polynomials

Polynomials are straightforward to write using superscripts ^ for exponents.

General Form:

$P(x) = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0$ $\rightarrow$ $P(x) = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0$

Cubic Polynomial:

$y = 4x^3 - 2x^2 + 7x - 5$ $\rightarrow$ $y = 4x^3 - 2x^2 + 7x - 5$

Roots (Quadratic Formula):

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $\rightarrow$ $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Matrices

$$
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
$$

Enjoy writing math in your posts!