Examples

2.1(b) PROBLEMS UNDER THE INTERVAL (0, 21)

Example 2.1.b(1): Find the Fourier series expansion of period 21 for (1-x)2 in the range (0, 27). Deduce that

Example 2.1.b(2) Find the Fourier series expansion of f(x) = e^x in (0,2l)

Solution: Let the Fourier series be

Example 2.1.b(3) Find the Fourier series of

Solution: Let the Fourier series be

Example 2.1.b(4) Find the Fourier expansion of

Example 2.1.b(5): Find the Fourier series of the function

f(x)) =2x-x for 0 < x <3 and f(x+3) = f(x).

Example 2.1.b(7): Obtain Fourier series for f(x) of period 21 and defined as follows