# 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

**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?

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