Name:

MATH 285 Section N1
Fall 2001
Quiz 5

Please answer all questions on this sheet (note that there is a question on the back as well). You must show your work to obtain full credit. 10 points are possible. Good luck!

1.

(5 points) Find the Fourier series of the period function with f(t)=0 for 0< t< p and f(t)=1 for p< t< 2 p

2.

(5 points) Consider the period 6 function with

(a)

Write the integrals giving the Fourier coefficients of the Fourier series of f(t). Do not evaluate the integrals.

(b)

Call these coefficients a_n,b_n as usual. Express the Fourier series in terms of a_n,b_n.

(c)

Find the value to which the Fourier series converges for t=0,1,3.