Chapter 13.5, Problem 1P

1. Compute numerically the coefficients (5.16) of the first three terms of the series (5.11) for the steady-state temperature in a solid semi-infinite cylinder when $u=0$ at $r=1,$ and $u=100$ at $z=0.$ Find $u$ at $r=\frac{1}{2},z=1$.
2. In part (a), if $u=0$ at $r=10$ and $u=100$ at $z=0,$ find $u$ at $r=5,z=10$
3. What is the relation between parts (a) and (b)?Hint: Suppose in part (a) that the length units for $r$ and $z$ are centimeters. Consider the identical physics problem but with distances measured in millimeters, and compare part (b). Note that in equation $(5.10),r/a$ and $z/a$ are just measurements as multiples of the radius $a$.