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)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fedbd0a5d-0e43-41b1-a3de-4c5dcfca7a91%2F738c14b1-f3d6-4966-97a3-848215522d0f%2Funfr50l_processed.jpeg&w=3840&q=75)
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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