MediumChange of variables

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §14.4 Cylindrical and Spherical Coordinates, #27 · Multivariable Calculus · Change of variables

Compute … in the first cosine law and show from Figure 14.18…

Problems, on the attraction of a sphere, use Figure 14.18 and the law of cosines $q^{2} = D^{2} - 2 ρ D cos ϕ + ρ^{2} = u$ .

Compute $\partial q / \partial D$ in the first cosine law and show from Figure 14.18 that it equals $cos α$ . Then the derivative of equation (2) with respect to $D$ is a shortcut to Newton's equation (3).

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §14.4 Cylindrical and Spherical Coordinates, #27

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