Differentiation and integration of Fourier series.

Description
How can a Fourier series be differentiated and integrated is explained with the help of explained in this video lecture. Integration of the Fourier series of the squarewave is described. From this it can be concluded that it is not true in general that the integral of a periodic function is periodic. The integral is periodic if the average value of the function is zero. Harmonic oscillator with periodic forcing is discussed. From the discussion It turns out that your ear hears only the amplitudes of the various fourier components, or harmonics, not their relative phases. Salmon function is introduced by Prof. Arthur Mattuck.
Prof. Arthur Mattuck, Maths, 18.03.Differential Equations, Spring 2010: 17: Finding Particular Solutions via Fourier Series: Massachusetts Institute of Technology: MIT Open Course Ware),http://ocw.mit.edu (Accessed November 8, 2011). License: Creative Commons BY-NC-SA: http://ocw.mit.edu/terms/#cc