KaTeX Examples

This page collects KaTeX examples so that authors can quickly validate typography and the shared macro set. Every block below renders server-side via remark-math and rehype-katex with copy-paste friendly MathML and TeX.

Inline vs display

Inline math keeps equations in the flow of text, such as $E=mc^2$ or the unit vector $\vu{n}$. Display math is set apart for emphasis:

$$\vb{F} = m \vb{a}$$

Use \ifrac{a}{b} or \tfrac{a}{b} for inline fractions like $\ifrac{a}{b}$ and \frac{a}{b} for display:

$$\frac{1}{2}mv^2 + mgh = \text{const}$$

Limits and derivatives

The macros include differential operators for concise notation:

• Velocity: $\dv{\vb{r}}{t}$
• Heat flow: $\pdv{Q}{t}$
• Gradient: $\grad T$
• Divergence: $\divergence \vb{E}$
• Curl: $\curl \vb{B}$

A standard limit rendered with left-aligned display math:

$$\lim_{x \to 0} \frac{\sin x}{x} = 1$$

Matrices and vectors

$$\vb{v} = \begin{pmatrix} v_x \\ v_y \\ v_z \end{pmatrix}, \quad \mathbf{A} = \begin{bmatrix} 2 & 1 & 0 \\ 1 & 3 & -1 \\ 0 & -1 & 4 \end{bmatrix}$$

Vectors in inline math look like $\vb{p}$ while unit vectors such as $\vu{z}$ keep the hat aligned with the bold letter.

Absolute values, norms, and delimiters

$$\abs{\vb{v}} = \norm{\vb{v}} = \sqrt{v_x^2 + v_y^2 + v_z^2}, \qquad \qty{E = mc^2}, \quad \qtyb{0 \leq t \leq T}, \quad \qtyc{ x \in \R }$$

Graphing island

The <Graph2D /> component renders lightweight function plots on the client using Plotly. Expressions are parsed with expr-eval so authors can experiment with quick sketches:

Try a polynomial with asymptotes:

Copy the original TeX

Thanks to the copy-tex plugin, selecting $\int_0^{\pi} \sin x\,\dd x$ in the rendered output copies the raw TeX (\int_0^{\pi} \sin x\,\dd x). This makes it easy to reuse formulas across lectures without retyping them.

Keep this gallery handy when tuning future typography or testing new macros.