The Azimuthal Unit Vector

In this post, I write the azimuthal unit vector $\vec{e}_{\phi}$ in terms of Cartesian coordinates. Here, $\phi$ is the azimuthal angle in the $x-y$ plane. As noted in this post, $\vec{e}_{\phi}$ points in the direction…

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A Right Handed Spherical Coordinate System

This post introduced the following questions. What direction does $\vec{e}_{\phi}$ point? Modern convention dictates that $\vec{e}_{\phi}$ should point in the direction of increasing $\phi$, but what is the reason for this convention? If there are…

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Reasoning about Left and Right Handed Coordinate Systems

A coordinate system can be defined by three perpendicular unit vectors. If the coordinate system is Cartesian, which direction does the $+x$ axis point? To resolve this problem, I define an orientation–a coordinate system…

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The Crux of Calculus

Define $\Delta x \equiv x_2 – x_1$, to be consistent with this post. Similarly, define $\Delta y \equiv y_2 – y_1$ and $\Delta z \equiv z_2 – z_1$. The Cartesian coordinates are $x$, $y$,…

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