SearchOnMath

The binomial theorem, making use of the well-known binomial coefficients, allows expressing \((x+y)^n\) as a sum: \((x+y)^n=\sum_{k=0}^{n} \binom{n}{k} x^k y^{n-k}\).

Maxwell's equations in a vacuum describe a wave propagating at speed \(c\) as the interaction of electric field \(E\) and magnetic field \(B\): \(\nabla \cdot E = 0\), \(\nabla \times E = -\frac{\partial B}{\partial t}\), \(\nabla \cdot B = 0\), \(\nabla \times B = \frac{1}{c^2} \frac{\partial E}{\partial t}\).

Complicated convolution operations become simple multiplications via the Laplace transform \(F(s) = \int_{-\infty}^{\infty}f(x)e^{-s x}dx\) for function \(f\).