Assignment

Math 460

Test 2

Show all the work.

1) Find the type, transform to normal form, and solve the following PDE:

a)

b)

c)

2) If the rod is fastened at one end, and free at the other, , we have and

= 0. Show that the motion corresponding to initial displacement and initial velocity zero is

, where

, and

3) Using the equation (6) in page 569 of our text, obtain the solution of

in integral form satisfying the initial condition

.

4) Represent , a and b are arbitrary, by the double Fourier series

.