Assignment # 2

Math 513

1) Find Fourier cosine and Fourier sine series for the following functions in [0,]

a)

b) f(x) = sin x

c) f(x) = cos x

2) Find Fourier series in [-] for following f(x)

a)

b)

c)

3) Consider following

f(x) = x , an odd function in

Find its Fourier series in , Fourier sine and cosine series in [0,]. Compare and comment on the results.

Similarly consider f(x) =

Find the three series in the respective intervals indicated above.