P11) Compute the Fourier coefficients

,

where if and if . Use your answer to write down both the complex Fourier series of

as well the real Fourier series of

.

P12) Same as P11), but with if and if .

P13) Same as P11), but with where . (Hint: You can use your solution to P12) here. What’s the relation between the functions of P12) and P13)? )

P13) Same as P11), but with . Differentiate the Fourier series you just computed term by term and compare with the Fourier series of . (We computed the Fourier series of the sawtooth wave in class.) Could you have used the Fourier series for the sawtooth wave to deduce that of instead of computing it “from scratch”?

P14) Same as P11), but with if and if .