# Mathematics Showcase
This document demonstrates math expression support in PDF conversion.
## Inline Math
The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ for solving equations.
Einstein's famous equation: $E = mc^2$
The Pythagorean theorem: $a^2 + b^2 = c^2$
## Math Blocks
### Calculus
$$
\int_a^b f(x) dx = F(b) - F(a)
$$
$$
\frac{d}{dx} x^n = nx^{n-1}
$$
### Linear Algebra
$$
\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}
$$
### Series and Summations
$$
\sum_{i=1}^{n} i = \frac{n(n+1)}{2}
$$
$$
\prod_{i=1}^{n} i = n!
$$
### Limits
$$
\lim_{x \to \infty} \frac{1}{x} = 0
$$
### Greek Letters in Math
$$
\alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta
$$
$$
\pi \approx 3.14159, \quad e \approx 2.71828
$$
### Complex Equations
$$
\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}
$$
$$
\nabla \cdot \vec{B} = 0
$$
### Statistics
$$
\mu = \frac{1}{n} \sum_{i=1}^{n} x_i
$$
$$
\sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \mu)^2
$$
### Set Theory
$$
A \cup B, \quad A \cap B, \quad A \subseteq B
$$
$$
\forall x \in \mathbb{R}, \exists y \in \mathbb{R} : y > x
$$
## Mixed Text and Math
When solving $ax^2 + bx + c = 0$, we use the quadratic formula to find:
$$
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
$$
The discriminant $\Delta = b^2 - 4ac$ determines the nature of the roots.