Math & Physics Essentials

Pythagorean theorem

$a^2 + b^2 = c^2$

Quadratic Formula

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Einstein's Mass-Energy Equivalence

$E = mc^2$

Fundamental Theorem of Calculus

$\int_{a}^{b} f(x) \,dx = F(b) - F(a)$

Normal Distribution Formula

$f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}$

Infinite Series

$\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}$

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