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The function v (x, y) satisfies the Laplace's equation in rectangular coordinates (x, y) and for points within the rectangle x=0, x= 0, y = 0, y =b, it satisfies the conditions v (0, y) = v(a, y) = v(x, b) = 0, and v (x, 0)=xía-x), 0

The function v (x, y) satisfies the Laplace's equation in rectangular coordinates (x, y) and for points within the rectangle x=0, x= 0, y = 0, y =b, it satisfies the conditions v (0, y) = v(a, y) = v(x, b) = 0, and v (x, 0)=xía-x), 0

Applications and Investigations in Earth Science (9th Edition)
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Chapter1: The Study Of Minerals
Section: Chapter Questions
Problem 1LR
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The function v (x, y) satisfies the Laplace's equation in rectangular coordinates (x, y) and for points within the rectangle x=0, x=a, y = 0, y =b, it satisfies the conditions v (0, y) = v(a, y) = v(x, b) = 0 and v (x, 0) = xía-x), 0<x<a. Show that v (x, y) is given by v(x, y) = 842 Σ Ла0 sin (2n +1) mxlu sinh (2n + 1) (b - y)la sinh (2n + 1) blu (2n + 1)³
Transcribed Image Text:The function v (x, y) satisfies the Laplace's equation in rectangular coordinates (x, y) and for points within the rectangle x=0, x=a, y = 0, y =b, it satisfies the conditions v (0, y) = v(a, y) = v(x, b) = 0 and v (x, 0) = xía-x), 0<x<a. Show that v (x, y) is given by v(x, y) = 842 Σ Ла0 sin (2n +1) mxlu sinh (2n + 1) (b - y)la sinh (2n + 1) blu (2n + 1)³
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