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A unitary linear operator which resolves a function on $\mathbb{R}^N$ into a linear superposition of "plane wave functions". Most often used in physics for calculating the response of a time shift invariant linear system as the sum of its response to time harmonic excitation or for transforming a quantum state in position co-ordinates into one in momentum co-ordinates and contrawise. There is also a discrete, fast Fourier transform for discretised data.

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Kolb and Turner's expresion for number density Eqn. (3.46) and pressure in Eqn. (3.48)

I think relation (2) can be derived the following way. Consider an element of surface $\delta S$ with its unit vector $\vec n$. The particles that will collide with it during a time ${\rm d} t$ lie in …
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