MathJax Cheatsheet

LaTeX math syntax · rendered in-browser via MathJax 3  ·  Inline: \( ... \)  ·  Display block: \[ ... \]

Integrals

Syntax → Rendered
\int_1^2 x^2 \, dx \( \int_1^2 x^2 \, dx \)
\int_0^\infty e^{-x} \, dx \( \int_0^\infty e^{-x} \, dx \)
\int_{-\infty}^{\infty} f(x) \, dx \( \int_{-\infty}^{\infty} f(x) \, dx \)
\iint_D f(x,y) \, dA \( \iint_D f(x,y) \, dA \)
\oint_C \mathbf{F} \cdot d\mathbf{r} \( \oint_C \mathbf{F} \cdot d\mathbf{r} \)

Sums & Products

Syntax → Rendered
\sum_{i=0}^{n} x_i \( \sum_{i=0}^{n} x_i \)
\sum_{k=1}^{\infty} \frac{1}{k^2} \( \sum_{k=1}^{\infty} \frac{1}{k^2} \)
\prod_{j=1}^{N} p_j \( \prod_{j=1}^{N} p_j \)

Fractions & Roots

Syntax → Rendered
\frac{a}{b} \( \frac{a}{b} \)
\frac{x^2 + 1}{2x - 3} \( \frac{x^2 + 1}{2x - 3} \)
\sqrt{x} \( \sqrt{x} \)
\sqrt[3]{x} \( \sqrt[3]{x} \)
\sqrt{\frac{a}{b}} \( \sqrt{\frac{a}{b}} \)

Derivatives

Syntax → Rendered
\frac{dy}{dx} \( \frac{dy}{dx} \)
\frac{d^2y}{dx^2} \( \frac{d^2y}{dx^2} \)
\frac{\partial f}{\partial x} \( \frac{\partial f}{\partial x} \)
\frac{\partial^2 f}{\partial x \partial y} \( \frac{\partial^2 f}{\partial x \partial y} \)
\nabla f \( \nabla f \)
\nabla^2 f \( \nabla^2 f \)

Limits

Syntax → Rendered
\lim_{x \to 0} f(x) \( \lim_{x \to 0} f(x) \)
\lim_{x \to \infty} \frac{1}{x} \( \lim_{x \to \infty} \frac{1}{x} \)
\lim_{x \to 0^+} \ln x \( \lim_{x \to 0^+} \ln x \)

Greek Letters

Lowercase
\alpha \beta \gamma\( \alpha \; \beta \; \gamma \)
\delta \epsilon \zeta\( \delta \; \epsilon \; \zeta \)
\eta \theta \lambda\( \eta \; \theta \; \lambda \)
\mu \nu \xi\( \mu \; \nu \; \xi \)
\pi \rho \sigma\( \pi \; \rho \; \sigma \)
\tau \phi \chi \psi \omega\( \tau \; \phi \; \chi \; \psi \; \omega \)
Uppercase
\Gamma \Delta \Theta\( \Gamma \; \Delta \; \Theta \)
\Lambda \Xi \Pi\( \Lambda \; \Xi \; \Pi \)
\Sigma \Phi \Psi \Omega\( \Sigma \; \Phi \; \Psi \; \Omega \)

Common Operators & Symbols

Operators
\times\( \times \)
\cdot\( \cdot \)
\div\( \div \)
\pm\( \pm \)
\leq \geq\( \leq \; \geq \)
\neq\( \neq \)
\approx\( \approx \)
\equiv\( \equiv \)
\propto\( \propto \)
Arrows & Sets
\to \rightarrow\( \to \)
\leftarrow\( \leftarrow \)
\leftrightarrow\( \leftrightarrow \)
\Rightarrow\( \Rightarrow \)
\in \notin\( \in \; \notin \)
\subset \subseteq\( \subset \; \subseteq \)
\cup \cap\( \cup \; \cap \)
\infty\( \infty \)

Display Block Examples \[ ... \]

Full equations — centred and larger
\[ \int_0^\infty e^{-x^2} dx = \frac{\sqrt{\pi}}{2} \] \[ \int_0^\infty e^{-x^2} dx = \frac{\sqrt{\pi}}{2} \]
\[ E = mc^2 \] \[ E = mc^2 \]
\[ \nabla^2 \phi = \frac{1}{c^2} \frac{\partial^2 \phi}{\partial t^2} \] \[ \nabla^2 \phi = \frac{1}{c^2} \frac{\partial^2 \phi}{\partial t^2} \]
\[ \sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6} \] \[ \sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6} \]
\[ F = G \frac{m_1 m_2}{r^2} \] \[ F = G \frac{m_1 m_2}{r^2} \]

Vectors & Notation

Vector styles
\mathbf{F}\( \mathbf{F} \)
\vec{v}\( \vec{v} \)
\hat{r}\( \hat{r} \)
\hat{\phi}\( \hat{\phi} \)
\hat{z}\( \hat{z} \)
\bar{x}\( \bar{x} \)
\tilde{x}\( \tilde{x} \)
\dot{x} \;\; \ddot{x}\( \dot{x} \;\; \ddot{x} \)
Vector operations
\mathbf{A} \cdot \mathbf{B}\( \mathbf{A} \cdot \mathbf{B} \)
\mathbf{A} \times \mathbf{B}\( \mathbf{A} \times \mathbf{B} \)
\nabla \cdot \mathbf{F}\( \nabla \cdot \mathbf{F} \)
\nabla \times \mathbf{F}\( \nabla \times \mathbf{F} \)
\nabla^2 f\( \nabla^2 f \)
|\mathbf{v}|\( |\mathbf{v}| \)
\left| \frac{a}{b} \right|\( \left| \frac{a}{b} \right| \)

Matrices

Syntax → Rendered
\begin{pmatrix} a & b \\ c & d \end{pmatrix} \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \)
\begin{vmatrix} a & b \\ c & d \end{vmatrix} \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \)
\begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} \( \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} \)

Aligned Equations (align environment)

Use & as alignment point, \\ for new line
\begin{align} x &= a + b \\ y &= c + d \end{align} \[\begin{align} x &= a + b \\ y &= c + d \end{align}\]
\begin{align} f(x) &= x^2 + 2x + 1 \\ &= (x+1)^2 \end{align} \[\begin{align} f(x) &= x^2 + 2x + 1 \\ &= (x+1)^2 \end{align}\]

Maxwell's Equations — Cylindrical Coordinates (benchmark)

Gauss's law for E · \( \nabla \cdot \mathbf{E} = \rho/\varepsilon_0 \)
\frac{1}{r}\frac{\partial(r E_r)}{\partial r} + \frac{1}{r}\frac{\partial E_\phi}{\partial \phi} + \frac{\partial E_z}{\partial z} = \frac{\rho}{\varepsilon_0} \[ \frac{1}{r}\frac{\partial(r E_r)}{\partial r} + \frac{1}{r}\frac{\partial E_\phi}{\partial \phi} + \frac{\partial E_z}{\partial z} = \frac{\rho}{\varepsilon_0} \]
Gauss's law for B · \( \nabla \cdot \mathbf{B} = 0 \)
\frac{1}{r}\frac{\partial(r B_r)}{\partial r} + \frac{1}{r}\frac{\partial B_\phi}{\partial \phi} + \frac{\partial B_z}{\partial z} = 0 \[ \frac{1}{r}\frac{\partial(r B_r)}{\partial r} + \frac{1}{r}\frac{\partial B_\phi}{\partial \phi} + \frac{\partial B_z}{\partial z} = 0 \]
Faraday's law · \( \nabla \times \mathbf{E} = -\partial\mathbf{B}/\partial t \) — z-component shown
\frac{1}{r}\frac{\partial(r E_\phi)}{\partial r} - \frac{1}{r}\frac{\partial E_r}{\partial \phi} = -\frac{\partial B_z}{\partial t} \[ \frac{1}{r}\frac{\partial(r E_\phi)}{\partial r} - \frac{1}{r}\frac{\partial E_r}{\partial \phi} = -\frac{\partial B_z}{\partial t} \]
Ampère–Maxwell law · \( \nabla \times \mathbf{B} = \mu_0\mathbf{J} + \mu_0\varepsilon_0\,\partial\mathbf{E}/\partial t \) — z-component shown
\frac{1}{r}\frac{\partial(r B_\phi)}{\partial r} - \frac{1}{r}\frac{\partial B_r}{\partial \phi} = \mu_0 J_z + \mu_0\varepsilon_0 \frac{\partial E_z}{\partial t} \[ \frac{1}{r}\frac{\partial(r B_\phi)}{\partial r} - \frac{1}{r}\frac{\partial B_r}{\partial \phi} = \mu_0 J_z + \mu_0\varepsilon_0 \frac{\partial E_z}{\partial t} \]

Other Useful Physics Constructs

Syntax → Rendered
\left( \frac{\partial^2}{\partial r^2} + \frac{1}{r}\frac{\partial}{\partial r} + \frac{1}{r^2}\frac{\partial^2}{\partial\phi^2} + \frac{\partial^2}{\partial z^2} \right) f \[ \left( \frac{\partial^2}{\partial r^2} + \frac{1}{r}\frac{\partial}{\partial r} + \frac{1}{r^2}\frac{\partial^2}{\partial\phi^2} + \frac{\partial^2}{\partial z^2} \right) f \]
\oint_S \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{\text{enc}}}{\varepsilon_0} \[ \oint_S \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{\text{enc}}}{\varepsilon_0} \]
\hbar \frac{\partial \psi}{\partial t} = \hat{H}\psi \[ \hbar \frac{\partial \psi}{\partial t} = \hat{H}\psi \]
e^{i\theta} = \cos\theta + i\sin\theta \[ e^{i\theta} = \cos\theta + i\sin\theta \]
\int_V \nabla \cdot \mathbf{F} \, dV = \oint_S \mathbf{F} \cdot d\mathbf{A} \[ \int_V \nabla \cdot \mathbf{F} \, dV = \oint_S \mathbf{F} \cdot d\mathbf{A} \]

Setup — paste into your <head>

Minimal MathJax 3 include
<script src="https://cdn.jsdelivr.net/npm/ mathjax@3/es5/tex-chtml.js"> </script> One script tag. No configuration needed for standard use. Loads asynchronously; equations render after page load. For local/offline use, npm install mathjax and serve from your own path.
Spacing inside math: \, thin space (before dx)  ·  \; medium space  ·  \quad large space  ·  \! negative thin space

Grouping: curly braces { } group tokens — x^2 gives x² but x^{2n} gives x²ⁿ. Same for subscripts.

Auto-sizing brackets: \left( ... \right) scales to content height — essential for fractions inside brackets.

Text inside math: \text{enc} for roman subscript labels, e.g. Q_{\text{enc}} → \( Q_{\text{enc}} \)

Matrices: columns separated by &, rows by \\ — same as the align environment.

Common constants: \varepsilon_0 → \( \varepsilon_0 \)  ·  \mu_0 → \( \mu_0 \)  ·  \hbar → \( \hbar \)  ·  \infty → \( \infty \)