Investigating the Meaning of a Function to the Right of the Del Operator

Let $F(x,y,z) \equiv f(x) g(y) h(z)$. In this previous post, $\vec{\nabla}F(x,y,z)$ was written in terms of spherical coordinates and unit vectors for a spherical coordinate system. The corresponding equation was found to be $ \vec{\nabla}F(x,y,z) = \vec{e}_r…

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Writing Del in Terms of Spherical Coordinates

Objective The objective of this post is to investigate the validity of (6) in Reference 2. In this reference, (6) is del is written in terms of spherical coordinates and spherical unit vectors. Partial…

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Writing Unit Vectors for a Cartesian Coordinate System in Terms of Unit Vectors for a Spherical Coordinate System

Objective of this Post The objective of this post is to form (4) in this reference. Partial Derivatives Relating Cartesian Coordinates to Spherical Coordinates Suppose $F(x,y,z) \equiv f(x) g(y) h(z)$. In the previous post, the following…

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How a Multivariable Function Changes with Respect to the Cartesian Coordinates

Suppose $F(x,y,z) \equiv f(x) g(y) h(z)$. This post shows how to calculate a partial derivative of a multivariable function $F(x,y,z)$ with respect to each Cartesian coordinates. The resulting expressions are in spherical coordinates. In previous…

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