Help with Writing Formulas and Equations

This guide provides a comprehensive overview of how to write mathematical notation in Notebook using LaTeX syntax powered by the KaTeX engine.

Basics: Delimiters

Notebook uses dollar signs as delimiters for mathematical expressions.

Inline Math

Use single dollar signs $ ... $ for math that should appear within a sentence.

  • Input: The energy-mass relation is `$E = mc^2$` in physics.
  • Rendered: The energy-mass relation is E=mc2E = mc^2 in physics.

Block Math

Use double dollar signs $$ ... $$ for math that should be centered and on its own line.

  • Input:
    $$
a^2 + b^2 = c^2
$$
  • Rendered:a2+b2=c2a^2 + b^2 = c^2

Common Mathematical Structures

Superscripts and Subscripts

Use ^ for superscripts and _ for subscripts. Use curly braces {} for multiple characters.

  • Input: $x_{i}^2 + y_{i}^2 = R^2$
  • Rendered: xi2+yi2=R2x_{i}^2 + y_{i}^2 = R^2

Fractions

Use \frac{numerator}{denominator}.

  • Input: $\frac{1}{n} \sum_{i=1}^{n} x_i$
  • Rendered: 1n∑i=1nxi\frac{1}{n} \sum_{i=1}^{n} x_i

Roots

Use \sqrt{...} for square roots and \sqrt[n]{...} for n-th roots.

  • Input: $\sqrt{b^2 - 4ac}$ and $\sqrt[3]{x}$
  • Rendered: b2−4ac\sqrt{b^2 - 4ac} and x3\sqrt[3]{x}

Summations and Integrals

  • Summation: \sum_{lower}^{upper}
  • Integral: \int_{lower}^{upper}
  • Input:
    $$
\int_{0}^{\infty} e^{-x^2} dx = \frac{\sqrt{\pi}}{2}
$$
  • Rendered:∫0∞e−x2dx=π2\int_{0}^{\infty} e^{-x^2} dx = \frac{\sqrt{\pi}}{2}

Greek Letters and Symbols

Symbol Command Symbol Command
α\alpha \alpha β\beta \beta
γ\gamma `\gamma$ δ\delta \delta
θ\theta \theta λ\lambda \lambda
π\pi \pi ω\omega `\omega$
Δ\Delta \Delta Ω\Omega \Omega
ℏ\hbar \hbar ∞\infty \infty

Advanced Formatting

Matrices

Matrices use the matrix, pmatrix (parentheses), or bmatrix (brackets) environments.

  • Input:
    $$
\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}
$$
  • Rendered:[abcd]\begin{bmatrix} a & b \\ c & d \end{bmatrix}

Multi-line Equations

Use the aligned environment for multi-line derivations.

  • Input:
    $$
\begin{aligned}
(x+y)^2 &= (x+y)(x+y) \\
        &= x^2 + xy + yx + y^2 \\
        &= x^2 + 2xy + y^2
\end{aligned}
$$
  • Rendered:(x+y)2=(x+y)(x+y)=x2+xy+yx+y2=x2+2xy+y2\begin{aligned} (x+y)^2 &= (x+y)(x+y) \\ &= x^2 + xy + yx + y^2 \\ &= x^2 + 2xy + y^2 \end{aligned}

Tips for Success

  1. No Spaces in Delimiters: While Notebook is configured to be flexible, it's best practice not to have spaces between the $ and your math (e.g., use $x$ not $ x $).
  2. Escaping: If you want to use a literal dollar sign in your text, use \$.
  3. KaTeX Support: Notebook uses KaTeX, which is faster than MathJax but supports a slightly smaller subset of LaTeX. You can find a full list of supported functions on the KaTeX website.