Covered today: The wave equation - Section 10.6. For those not in class, read the entire section, except for the part labelled "Justification of the Solution."

For next time: 10.6 - 1,2,3,6,7

Transparencies from class:

• Suppose you have a string which is 10 cm long and has a=1. Suppose you initially configure it into the shape of
  
  $$f(x)=\left\{\begin{array}{cl} x & 0 < x < 1\\ 2-x & 1 < x< 2\\ 0 & x>2 \end{array}\right.$$
  
  
  and then you release it. Find u(x,t).

• Suppose you have a string which is 10 cm long and has a=1. Suppose you initially configure it into the shape of
  
  $$f(x)=\left\{\begin{array}{cl} 0 & 0 < x < 4\\ x-4 & 4 < x< 5\\ -x+6 & 5<x<6\\ 0 & 6<x<10 \end{array}\right.$$
  
  
  and then you release it. Find u(x,t).

Maple commands:

The Maple commands from today were all very similar to those from last time. See the Nov 22 daily log. The only new one introduced this time was animate.

After you've got your u(x,t), type

with(plots);

and then

animate(u(x,t), x=0..10, t=0..20);