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A rod of length L coincides with the interval [0, L] on the x-axis. Set up the boundary-value problem for the temperature u(x, t). The left end is at temperature sin(πt/L), the right end is held at zero, and there is heat transfer from the lateral surface of the rod into the surrounding medium held at temperature zero. The initial temperature is f(x) throughout. кози - hu = ax² u(0, t) = ди at 0 < x < L, t > 0, h a constant , u(L, t) = = f(x), 0 0

A rod of length L coincides with the interval [0, L] on the x-axis. Set up the boundary-value problem for the temperature u(x, t). The left end is at temperature sin(πt/L), the right end is held at zero, and there is heat transfer from the lateral surface of the rod into the surrounding medium held at temperature zero. The initial temperature is f(x) throughout. кози - hu = ax² u(0, t) = ди at 0 < x < L, t > 0, h a constant , u(L, t) = = f(x), 0 0

Calculus For The Life Sciences
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.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 15E
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A rod of length L coincides with the interval [0, L] on the x-axis. Set up the boundary-value problem for the temperature u(x, t). The left end is at temperature sin(πt/L), the right end is held at zero, and there is heat transfer from the lateral surface of the rod into the surrounding medium held at temperature zero. The initial temperature is f(x) throughout. кази - hu = əx² u(0, t) = au at 0 < x < L, t > 0, h a constant I u(L, t) = = f(x), 0 < x <L , t > 0
Transcribed Image Text:A rod of length L coincides with the interval [0, L] on the x-axis. Set up the boundary-value problem for the temperature u(x, t). The left end is at temperature sin(πt/L), the right end is held at zero, and there is heat transfer from the lateral surface of the rod into the surrounding medium held at temperature zero. The initial temperature is f(x) throughout. кази - hu = əx² u(0, t) = au at 0 < x < L, t > 0, h a constant I u(L, t) = = f(x), 0 < x <L , t > 0
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