# 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.
