(a) Find the series solution for u(r, u) in Example 1 when

Chapter 13, Problem 13.1.20

(choose chapter or problem)

(a) Find the series solution for u(r, u) in Example 1 when (b) Use a CAS or a graphing utility to plot the partial sum S5(r, u) consisting of the first five nonzero terms of the solution in part (a) for r 0.9, r 0.7, r 0.5, r 0.3, and r 0.1. Superimpose the graphs on the same coordinate axes. (c) Approximate the temperatures u(0.9, 1.3), u(0.7, 2), u(0.5, 3.5), u(0.3, 4), u(0.1, 5.5). Then approximate u(0.9, 2p 1.3), u(0.7, 2p 2), u(0.5, 2p 3.5), u(0.3, 2p 4), u(0.1, 2p 5.5). (d) What is the temperature at the center of the circular plate? Why is it appropriate to call this value the average temperature in the plate? [Hint: Look at the graphs in part (b) and look at the numbers in part (c).] u(1