The Laplacian operator is frequently used in multivariable calculus and partial differential equations. The calculation of the operator in Cartesian coordinates is straightforward and versions of the operator for polar, cylindrical, spherical, and other coordinate systems exist, though often just the result is present without the justifying steps. As an instructor of mathematics, I believe everyone (myself included) should derive the Laplacian in these other coordinate systems at least once in their mathematical career. The linked notes provide an outline of one method of deriving the Laplacian in spherical coordinates from the Laplacian in Cartesian coordinates.
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