Example of a sound (pressure) wave, showing how Fourier's expansion (for a function with period 2 Pi) can be used when your function has some different period. (Variable change, t -> 2 Pi t / T)
Discussion of averaging of functions. Definition of average value of f over an interval
New (graphical) trick for finding average value of sin^2(x).
Specific examples of averages, of both periodic and non-periodic functions
Where we're heading: the "trick" of Fourier, averaging both sides of his expansion (multiplied by a cos(nx) or sin(nx) first) gives you each of the Fourier coefficients, one at a time.
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