Problems

Exercise 1
Find the Fourier coefficients corresponding to the function

Possible solutions are:

1.

2.

a_n=0

3.

1.

2.

3.

Exercise 2
How should

be defined at x=-5, x=0 and x=5 in order that the Fourier series will converge to f(x) for ?

Possible solutions are:

1.

2.

3.

1.

2.

3.

Exercise 3
Expand f(x)=|x|, in a Fourier series if the period is

Possible solutions are:

1.

2.

3.

1.

2.

3.

Exercise 4 (Orthogonality conditions)
Let . Evaluate the following integrals:

Possible solutions are

1.

2.

3.

1.

2.

3.

Exercise 5
Find the Fourier representation (period ) of

Possible solutions are:

1.

2.

3.

1.

2.

3.

Exercise 6
Let f be piecewise continuous. Evaluate

Possible solutions are:

1.

2.

3.

1.

2.

3.

Exercise 7
From the Fourier series

the following equation can be obtained.

It is true that

1.

S(x) has a overshoot near by approximately .

2.

S(x) has a overshoot near x=0 by approximately .

3.

S(x) has no overshoot.

1.

2.

3.