MediumChange of variables

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §14.4 Cylindrical and Spherical Coordinates, #31 · Multivariable Calculus · Change of variables

In Figure 14.18b, it is not true that the areas on the…

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

In Figure 14.18b, it is not true that the areas on the surface are exactly proportional to $q^{2}$ and $Q^{2}$ . Why not? What happens to the second proof in Example 8?

This exercise builds on another exercise in its source book, which isn't shown here.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §14.4 Cylindrical and Spherical Coordinates, #31

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