The steady-state temperature in a hemisphere of radius r = c is determined from
0 < r < c, 0 < θ < π/2
u(r, π/2) = 0, 0 < r < c
u(r, θ) = f(θ), 0 < θ < π/2
Solve for u(r, θ). [Hint: Pn(0) = 0 only if n is odd. Also see Problem 20 in Exercises 11.5.]
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Chapter 13 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning