LaTeX Math Formulas: A Detailed Guide
LaTeX is the standard for typesetting mathematical formulas. You can use it in many environments, including Markdown, Jupyter Notebooks, Overleaf, and more.
1. Math Modes
Display Math: Use double dollar signs or \[ ... \]:
$$E = mc^2$$
or
\[ E = mc^2 \]
Renders as:
\[ E = mc^2 \]
Inline Math: Use single dollar signs:
$E = mc^2$
Renders as: \(E = mc^2\)
2. Basic Symbols
| Symbol | LaTeX Code | Renders as |
|---|---|---|
| Greek letter alpha | \alpha |
\(\alpha\) |
| Plus-minus | \pm |
\(\pm\) |
| Multiplication | \times |
\(\times\) |
| Division | \div |
\(\div\) |
| Infinity | \infty |
\(\infty\) |
| Partial derivative | \partial |
\(\partial\) |
3. Superscripts and Subscripts
- Superscript:
a^2→ \(a^2\) - Subscript:
a_1→ \(a_1\) - Combined:
x_i^2→ \(x_i^2\) - Grouping: Use curly braces for more than one character:
x^{10}→ \(x^{10}\)
4. Fractions, Roots, and Sums
- Fraction:
\frac{a}{b}→ \(\frac{a}{b}\) - Square root:
\sqrt{x}→ \(\sqrt{x}\) - n-th root:
\sqrt[n]{x}→ \(\sqrt[n]{x}\) - Sum:
\sum_{i=1}^n i→ \(\sum_{i=1}^n i\) - Product:
\prod_{i=1}^n i→ \(\prod_{i=1}^n i\) - Integral:
\int_0^1 x\,dx→ \(\int_0^1 x,dx\)
5. Common Functions
- Trigonometric:
\sin,\cos,\tan
Example:\sin^2 \theta + \cos^2 \theta = 1→ \(\sin^2 \theta + \cos^2 \theta = 1\) - Logarithms:
\log,\ln,\exp
Example:\ln(e^x) = x→ \(\ln(e^x) = x\)
6. Brackets and Parentheses
- Normal size:
(a+b)→ \((a+b)\) - Auto-sized:
\left( a+b \right)→ \(\left( a+b \right)\) - Other brackets:
\left[ ... \right]→ \(\left[ ... \right]\)\left\{ ... \right\}→ \(\left\{ ... \right\}\)\left| ... \right|→ \(\left| ... \right|\)
7. Matrices
\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}
Renders as:
\[ \begin{bmatrix} a & b \\ c & d \end{bmatrix} \]
Other environments: pmatrix (parentheses), vmatrix (vertical bars).
8. Special Symbols
| Symbol | Code | Renders as |
|---|---|---|
| Less or equal | \leq |
\(\leq\) |
| Greater or equal | \geq |
\(\geq\) |
| Not equal | \neq |
\(\neq\) |
| Approximately | \approx |
\(\approx\) |
| Element of | \in |
\(\in\) |
| Subset | \subset |
\(\subset\) |
9. Text in Math
To insert text in math mode:
\text{some text}
Example:\text{if } x > 0 → \(\text{if } x > 0\)
10. Example: Quadratic Formula
x = \frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a }
Renders as:
\[ x = \frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a } \]
11. Resources
- Overleaf LaTeX Math Guide
- Detexify (draw symbol to get LaTeX code)
- Comprehensive LaTeX Symbol List (PDF)
Note: In Markdown, LaTeX math is rendered only if the platform supports it.