LaTeX Examples

Differential Calcul Example:
- Finding the derivative of a function:

\frac{d}{d x} (x^{3} + 2 x) = 3 x^{2} + 2

Probability Example:
- Calculating the probability of an event:

P (A) = \frac{Number of favorable outcomes}{Total number of possible outcomes}

Integration Example:
- Evaluating a definite integral:

\int_{0}^{1} x^{2} d x = {[\frac{x^{3}}{3}]}_{0}^{1} = \frac{1}{3}

Series Example:
- Summing an infinite series:

\sum_{n = 1}^{\infty} \frac{1}{2^{n}} = 1

Matrix Example:
- Multiplication of two matrices:

(\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}) (\begin{matrix} 5 & 6 \\ 7 & 8 \end{matrix}) = (\begin{matrix} 19 & 22 \\ 43 & 50 \end{matrix})

Differential Equation Example:
- Solving a differential equation:

y^{'} = 2 x, y (0) = 1 ⟹ y (x) = x^{2} + 1

Set Theory Example:
- Union and intersection of sets:

(A \cup B) \cap C = A \cap C \cup B \cap C

Statistics Example:
- Calculating the mean of a dataset:

μ = \frac{1}{n} \sum_{i = 1}^{n} x_{i}

Vector Calculus Example:
- Gradient of a function:

\nabla f (x, y) = (\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y})

Complex Numbers Example:
- Multiplication of complex numbers:

(3 + 2 i) (1 - i) = 5 + i