Evaluate the Jacobian @.x; y; z/=@.R; ; /, where x D R sin c
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Evaluate the Jacobian @.x; y; z/=@.R; ; /, where x D R sin cos ; y D R sin sin ; and z D R cos : This is the transformat
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Evaluate the Jacobian @.x; y; z/=@.R; ; /, where x D R sin cos ; y D R sin sin ; and z D R cos : This is the transformation from Cartesian to spherical coordinates in 3-space that we discussed in Section 10.6. Near what points is the transformation one-to-one and hence invertible to give R, , and as functions of x, y, and z?
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