Week 12 (April 5 - April 9)

On Monday we will work on Review Questions and the take-home part of the test will be given out. On Wednesday, the take-home part of the test is due and the in-class part will be administered. On Friday, we will fill in some of the properties of the Fourier Transform that we omitted before the test.

Homework due on Monday, April 12 .

1. Finish the worksheet started in class on Friday.

The following problems were originally assigned last week For Problems 1 and 2, use Theorem 15.2 and the known Fourier transforms.

2. Find the Fourier transform of 5 [H(x - 3) - H(x - 11)]. (See Problem 3 in Section 15.1.)

3. Find the Fourier transform of 5 exp(-3(x - 5)²).

   .

4. Find a function f(x) such that the Fourier transform of f is F, where F(w) is the product of 1/(1 + iw)) and 1/(2 + iw). Do this two ways. First, expand F(w) by partial fractions and then use the linearity of the Fourier transform. Second, use the result on the convolution of a product. Make sure your two approaches give the same answer.

5. Find the Fourier transform of d/dx f(x), where f(x) = H(x) exp(-3x). (See Problem 5 in Section 15.2. Watch out for the jump discontinuity in f.)

Last modified: April 7, 1999