SearchOnMath

The fundamental theorem of calculus, \(f(x) = \frac{d}{dx}\int_{a}^{x}f(s)ds\), expresses the essential inverse relationship between the derivative and integral operators.

The heat equation, \(\frac{\partial \varnothing}{\partial t} = D \nabla^2 \varnothing\), uses the Laplacian of \(\varnothing\) to express diffusion through a medium.

Euler's identity, \(e^{i\pi}+1=0\), relates the imaginary unit and two famous irrational numbers in a way that is so simple it has been called beautiful.