The Fourier series of the function f(x)={1 for 0≤x<1, 2 for 1≤x<2, 0 otherwise can be determined. The function is piecewise continuous and repeats every 2 units, so the Fourier series will have terms of the form sin(nx) and cos(nx) where n is a positive integer. The coefficients of the terms can be determined by calculating the integral of the function times the basis functions over one period of 2 units.