Consider the heat equation ди Ət = J²u მ2 subject to the boundary conditions +u, 00, u(0,t) = u(L,t) = 0. Suppose 2πx 5πx u(x, 0) = 3 sin - - 8 sin L L where is a positive constant. a) Use separation of variables to solve the problem. b) Evaluate lim u(x,t). 0047 Does the value of the constant play a role in this limit? Explain.

Consider the heat equation ди Ət = J²u მ2 subject to the boundary conditions +u, 00, u(0,t) = u(L,t) = 0. Suppose 2πx 5πx u(x, 0) = 3 sin - - 8 sin L L where is a positive constant. a) Use separation of variables to solve the problem. b) Evaluate lim u(x,t). 0047 Does the value of the constant play a role in this limit? Explain.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.CR: Chapter 6 Review

Problem 38CR

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