Math Formulas with KaTeX

Inline math#

Einstein's mass–energy equivalence: $E = mc^2$ .

The quadratic formula gives roots $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .

The Gaussian integral:

\int_{-\infty}^{\infty} e^{-x^2}\, dx = \sqrt{\pi}

Euler's identity, often called the most beautiful equation in mathematics:

e^{i\pi} + 1 = 0

The fundamental theorem of calculus:

\int_a^b f'(x)\, dx = f(b) - f(a)

Taylor series expansion of $e^x$ around $x = 0$ :

e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots

For a matrix $A \in \mathbb{R}^{n \times n}$ , the determinant can be computed by cofactor expansion along the first row:

\det(A) = \sum_{j=1}^{n} (-1)^{1+j}\, a_{1j}\, M_{1j}

where $M_{1j}$ is the $(1,j)$ minor.