Half Range Series: Benefits & Applications

[matqkks]

If we have a standard function like x or x^2 defined between 0 and pi. Then why should we be interested in extending this function to give a Fourier series which resembles this function between 0 and pi? What is the whole purpose of this process? Does it have any real life application or is it just a mathematical exercise?

 

[Svein]

Then why should we be interested in extending this function to give a Fourier series which resembles this function between 0 and pi?

A sawtooth waveform is something you can observe in an oscilloscope and hear (if you run it through an audio amplifier). Between 0 and π it looks just like the function y = x.