Fourier series optimization opportunity

This note discusses the introduction of Fourier series as an immediate application of optimization of a function of more than one variable. Specifically, it is shown how the study of Fourier series can be motivated to enrich a multivariable calculus class. This is done through discovery learning and use of technology wherein students build the sine Fourier series for the simple function f(x) = x and then generalize to the nth term sine Fourier series for a general function, f(x). It is shown how the students can then explore the power of the Fourier series to represent functions.