Math¶

Mathematical notation rendered by MathJax. Enabled by the dollarmath and amsmath MyST extensions.

Note

See MathJax for setup instructions.

Inline Math¶

Embed math expressions within a line of text.

The equation \(E = mc^2\) describes mass-energy equivalence. The quadratic formula is \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).

The MyST syntax:

The equation $E = mc^2$ is inline math.

Display Math¶

Standalone equations centered on their own line.

\[ \int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi} \]

\[ \sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6} \]

The MyST syntax:

$$
\int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi}
$$

Labeled Equations¶

Add a label to reference an equation elsewhere in the document.

(1)¶\[e^{i\pi} + 1 = 0\]

Euler’s identity is shown in equation (1).

The MyST syntax:

```{math}
:label: euler
e^{i\pi} + 1 = 0
```

See equation {eq}`euler`.

Multi-line Equations¶

Use the amsmath environment for aligned multi-line equations.

(2)¶\[\begin{split}\begin{aligned} \nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \\ \nabla \cdot \mathbf{B} &= 0 \\ \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\ \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} \end{aligned}\end{split}\]

Maxwell’s equations (2) describe classical electromagnetism.

Piecewise Functions¶

\[\begin{split} f(x) = \begin{cases} x^2 & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases} \end{split}\]

The MyST syntax:

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

Matrix Notation¶

\[\begin{split} A = \begin{pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix} \end{split}\]

Different bracket styles:

Syntax	Brackets	Result
`pmatrix`	Parentheses	\(\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}\)
`bmatrix`	Square	\(\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}\)
`vmatrix`	Vertical bars	\(\begin{vmatrix} 1 & 2 \\ 3 & 4 \end{vmatrix}\)

Limits and Series¶

\[ \lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n = e \]

\[ \prod_{i=1}^{n} x_i = x_1 \cdot x_2 \cdots x_n \]

Common Symbols Reference¶

Greek Letters¶

Lowercase	Command	Uppercase	Command
\(\alpha\)	`\alpha`	\(A\)	`A`
\(\beta\)	`\beta`	\(B\)	`B`
\(\gamma\)	`\gamma`	\(\Gamma\)	`\Gamma`
\(\delta\)	`\delta`	\(\Delta\)	`\Delta`
\(\epsilon\)	`\epsilon`	\(E\)	`E`
\(\lambda\)	`\lambda`	\(\Lambda\)	`\Lambda`
\(\mu\)	`\mu`	\(M\)	`M`
\(\pi\)	`\pi`	\(\Pi\)	`\Pi`
\(\sigma\)	`\sigma`	\(\Sigma\)	`\Sigma`
\(\omega\)	`\omega`	\(\Omega\)	`\Omega`

Operators and Relations¶

Symbol	Command	Symbol	Command
\(\leq\)	`\leq`	\(\geq\)	`\geq`
\(\neq\)	`\neq`	\(\approx\)	`\approx`
\(\pm\)	`\pm`	\(\times\)	`\times`
\(\div\)	`\div`	\(\cdot\)	`\cdot`
\(\in\)	`\in`	\(\notin\)	`\notin`
\(\subset\)	`\subset`	\(\subseteq\)	`\subseteq`
\(\cup\)	`\cup`	\(\cap\)	`\cap`
\(\infty\)	`\infty`	\(\partial\)	`\partial`
\(\nabla\)	`\nabla`	\(\forall\)	`\forall`

Arrows¶

Symbol	Command	Symbol	Command
\(\rightarrow\)	`\rightarrow`	\(\leftarrow\)	`\leftarrow`
\(\Rightarrow\)	`\Rightarrow`	\(\Leftarrow\)	`\Leftarrow`
\(\leftrightarrow\)	`\leftrightarrow`	\(\Leftrightarrow\)	`\Leftrightarrow`
\(\mapsto\)	`\mapsto`	\(\implies\)	`\implies`

Tip

Use \text{} to include words inside math: \(P(\text{error}) < 0.05\)
Use \mathbf{} for bold vectors: \(\mathbf{v} = (v_1, v_2, v_3)\)
Use \, for thin spacing and \quad for wider spacing inside equations