Exploration of the Fourier Coefficient Applet
The Fourier Coefficients applet lets us explore the approximation of periodic functions by Fourier series. This is the opening screen of the applet. On the right, you see a series of sliders controlling coefficients. And they're the coefficients of the sine terms in a Fourier series, as you can see by clicking this formula box. So at this point, what we're studying is an odd function, a sine series, and the sliders let us control the coefficients of sine of k*t. If I click the cosine box, I'd see coefficients of the cosine functions. Let's go back to sine and start to play with the tool a little bit. What will happen if I move the b_2 slider? I should get multiples of the sine of 2t showing up on my graphing window. If I push b_2 to the right, I get positive multiples of the sine of 2t. The sine of 2t goes through two full periods when t ranges from 0 to 2pi. And if b_2 is negative, I get negative multiples of the sine of 2t. What happens if I change b_1 i...