Homework #5

Due on Friday of Week 5 at 5pm

1. A string of length L is stretched out in the x-direction, clamped at either end, and set into motion. The displacement of the string, u(x,t), must satisfy

a) Use separation of variables, and boundary conditions (which restrict the value of the separation constant) show that the general solution is

, where n = 1, 2, 3…

b) Is it okay that the general solution of a second order PDE has more than 2 linearly independent functions?

2. Butkov Problem 1 from Chapter 8.

3. Which of the following series converge?

a)

b)

c)

4. Evaluate these real-valued definite integrals using contour integration on the Argand plane

a)

b)