(a) Consider Example 1 with a 1, c 10, g(r) 0, and f (r) 1 r/10, 0 r 10. Use a CAS as an

Chapter 14, Problem 19

(choose chapter or problem)

(a) Consider Example 1 with a = 1, c = 10, g(r) = 0, and f(r) = 1 - r/10, 0 < r < 10. Use a CAS as an aid in finding the numerical values of the first three eigenvalues \(\lambda_{1}, \lambda_{2}, \lambda_{3}\) of the boundary-value problem and the first three coefficients \(A_{1}, A_{2}, A_{3}\) of the solution u(r, t) given in (9). Write the third partial sum \(S_{3}(r, t)\) of the series solution.

(b) Use a CAS to plot the graph of \(S_{3}(r, t)\) for t = 0, 4, 10, 12, 20.