Differential Equations Lecture Work Solutions 107

Differential Equations Lecture Work Solutions 107 - 4.5...

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4.5 Vibrating Circular Membrane Problems 1. Solve the heat equation u t ( r, θ, t )= k 2 u, 0 r<a , 0 <θ< 2 π, t > 0 subject to the boundary condition u ( a, θ, t ) = 0 (zero temperature on the boundary) and the initial condition u ( r, θ, 0) = α ( r, θ ) . 2. Solve the wave equation u tt ( r, t )= c 2 ( u rr + 1 r u r ) , u r ( a, t )=0 , u ( r, 0) = α ( r ) , u t ( r, 0) = 0 . Show the details. 3. Consult numerical analysis textbook to obtain the smallest eigenvalue of the above problem. 4. Solve the wave equation u tt ( r, θ, t ) c 2 2 u =0 , 0 r<a , 0 <θ< 2 π, t >
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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