Math 421:03, Fall 2002
Date: 30 October 2002
There are two (2) problems on this quiz. The other one is on the back of this page.
1.Formulate a boundary value problem modeling heat conduction in a thin bar of length if the left end is insulated and the right end is kept at a fixed temperate . The initial temperature distribution in the bar at is . (Just set up the problem and stop!)
2.Solve the boundary-value problem
This was enough as far as I was concerned. The simplification is tricker than on the homework, but can be done like this:
So clearly if is odd. If is even, can be written as , but depends on whether is even or odd! The numbers that can be written as 2 times an odd number look like . Therefore we have