For x sincos y sinsin z cos a Express 2 y 2 with , , , and ...

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For x = ÏsinÏ†cosÎ¸; y = ÏsinÏ†sinÎ¸; z = ÏcosÏ†: a/ Express âˆ‚^2/âˆ‚y^2 with Ï, Ï†,...

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For x = ÏsinÏ†cosÎ¸; y = ÏsinÏ†sinÎ¸; z = ÏcosÏ†:
a/ Express âˆ‚^2/âˆ‚y^2 with Ï, Ï†, Î¸, and their partials.
b/ Express âˆ‚^2/âˆ‚z^2 with Ï, Ï†, Î¸, and their partials.
c/ Express the Laplacian operator using sphericalcoordinates.

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For x = ÏsinÏ†cosÎ¸; y = ÏsinÏ†sinÎ¸; z = ÏcosÏ†: a/ Express âˆ‚^2/âˆ‚y^2 with Ï, Ï†,...

60.2K

Verified Solution

Question

Basic Math

For x = ÏsinÏ†cosÎ¸; y = ÏsinÏ†sinÎ¸; z = ÏcosÏ†:
a/ Express âˆ‚^2/âˆ‚y^2 with Ï, Ï†, Î¸, and their partials.
b/ Express âˆ‚^2/âˆ‚z^2 with Ï, Ï†, Î¸, and their partials.
c/ Express the Laplacian operator using sphericalcoordinates.

Answer & Explanation Solved by verified expert

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For x = ÏsinÏ†cosÎ¸; y = ÏsinÏ†sinÎ¸; z = ÏcosÏ†: a/ Express âˆ‚^2/âˆ‚y^2 with Ï, Ï†,...

60.2K

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Question

Basic Math

For x = ÏsinÏ†cosÎ¸; y = ÏsinÏ†sinÎ¸; z = ÏcosÏ†:a/ Express âˆ‚^2/âˆ‚y^2 with Ï, Ï†, Î¸, and their partials.b/ Express âˆ‚^2/âˆ‚z^2 with Ï, Ï†, Î¸, and their partials.c/ Express the Laplacian operator using sphericalcoordinates.

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For x = ÏsinÏ†cosÎ¸; y = ÏsinÏ†sinÎ¸; z = ÏcosÏ†: a/ Express âˆ‚^2/âˆ‚y^2 with Ï, Ï†,...

For x = ÏsinÏ†cosÎ¸; y = ÏsinÏ†sinÎ¸; z = ÏcosÏ†:
a/ Express âˆ‚^2/âˆ‚y^2 with Ï, Ï†, Î¸, and their partials.
b/ Express âˆ‚^2/âˆ‚z^2 with Ï, Ï†, Î¸, and their partials.
c/ Express the Laplacian operator using sphericalcoordinates.