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.