**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:

difference | |||

1 | 0 | -1 | 1 |

2 | -1 | 1 | -2 |

3 | 0 | -1 | 1 |

4 | 1 | 1 | 0 |

5 | 0 | -1 | 1 |

6 | -1 | 1 | -2 |

7 | 0 | -1 | 1 |

8 | 1 | 1 | 0 |

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

Matthew Leingang 2002-11-12