Examples

(a) PROBLEMS UNDER THE INTERVAL (0, 2 л)

Example 2.1.a(1): If f(x) = 1/2(л /x), find the Fourier series of period 2л in the interval (0,2 л). Hence deduce that

Example 2.1.a(2): Expand f(x) = x (2л-x) as Fourier series in (0, 2л) and hence deduce that the sum of 

Solution : Given: f(x) = x (2л - x) = 2πx-x2

Let the required Fourier series be

Example 2.1.a(3) Determine the Fourier series for the function f(x)=x of period 2л in 0 < x < 2л.

Solution : Let the required Fourier series be

Example 2.1.a(4): Expand f(x) e^ax as a Fourier series in (0, 2 л).

Solution :

Let the required Fourier series be

Example 2.1.a(5): Obtain the Fourier series of periodicity 2л for

Example 2.1.a (6): Expand in Fourier series of f(x) = x sin x for 0 < x < 2л and deduce the result

Example 2.1.a(7): Obtain the Fourier series for the function