Tuesday, August 6, 2024

My LaTeX Notes for Mathematical Expressions

This notes has been taken from this website.

\( x^n + y^n = z^n \)

\[ x^n + y^n = z^n \]

A LaTeX code should start with \( and end with \) if it is a inline equation. Otherwise, start with \[ and end with \].

These are power functions: \( x^n\),\( x^{a+b}\)
In physics, the mass-energy equivalence is stated by the equation \(E=mc^2\), discovered in 1905 by Albert Einstein.

This is a simple math expression \(\sqrt{x^2+1}\) inside text. \(\sqrt{x^{2+1}}\)

Greek letters \(\alpha \beta \gamma \rho \sigma \delta \epsilon\)

Binary operators \(\times \otimes \oplus \cup \cap\)

Relation operators \(< > \subset \supset \subseteq \supseteq\)

Others \(\int \oint \sum \prod\)

The expression \( x \leq 5 \) means that \( x \) is less than or equal to 5.

The expression \( y \geq 10 \) means that \( y \) is greater than or equal to 10.

\[ \int\limits_0^1 x^2 + y^2 \ dx \] \[ \int_0^1 x^2 + y^2 \ dx \] \[ a_1^2 + a_2^2 = a_3^2 \] \[ x^{2 \alpha} - 1 = y_{ij} + y_{ij} \] \[ (a^n)^{r+s} = a^{nr+ns} \] \[ \sum_{i=1}^{\infty} \frac{1}{n^s} = \prod_p \frac{1}{1 - p^{-s}} \]
\[a_{n_i}\] \[\int_{i=1}^n\] \[\sum_{i=1}^{\infty}\] \[\prod_{i=1}^n\] \[\cup_{i=1}^n\] \[\cap_{i=1}^n\] \[\oint_{i=1}^n\] \[\coprod_{i=1}^n\] Greek Letters \[\alpha A\] \[\beta B\] \[\gamma \Gamma\] \[\delta \Delta\] \[\epsilon \varepsilon E\] \[\zeta Z\] \[\eta H\] \[\theta \vartheta \Theta\] \[\iota I\] \[\kappa K\] \[\lambda \Lambda\] \[\mu M\] \[\nu N\] \[\xi \Xi\] \[o O\] \[\pi \Pi\] \[\rho \varrho P\] \[\sigma \Sigma\] \[\tau T\] \[\upsilon \Upsilon\] \[\phi \varphi \Phi\] \[\chi X\] \[\psi \Psi\] \[\omega \Omega\] \[\] \[\] \[\] \[\] \[\] \[\] \[\] \[\] \[\] \[\] \[\] \[\] \[\] \[\] \[\]

\(0 \leq r < b\)