First focus on the Cartesian coordinate $x$, which depends on the spherical coordinates $r,\theta,$ and $\phi$. For a function $f(x)$, the chain rule yields $ \frac{\partial f(x)}{\partial r} = ( \frac{\partial f}{\partial x} )…
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In this post, I relate coefficients of unit vectors to derivatives and to a Jacobian matrix that was used in a previous post. Unit Vectors Three unit vectors for a right-handed spherical coordinate…
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In this post, I find an expression for the radial unit vector, $\vec{e}_r$. The three unit vectors in the following digram form a right-handed spherical coordinate system. This unit vector is easier to…
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Consider a spherical coordinate system. Let a point be represented by $(r, \theta, \phi)$, in that order. Now that the order of the coordinates is established, I can define unit vectors that form…
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