The Fourier transform is one of the most important mathematical tools used for analyzing functions. Given an arbitrary function $$f(x)$$, with a real domain ($$x \in \mathbb{R}$$), we can express it as a linear combination of complex waves. The coefficients of the linear combination form a complex counterpart function, $$F(k)$$, defined in a wave-number domain ($$k \in \mathbb{R}$$). It turns out that $$F$$ is often much easier to deal with than $$f$$; in particular, differential equations for $$f$$ can often be reduced to algebraic equations for $$F$$, which are much easier to solve.