The Divergence And Gradient In Spherical Coordinates From Covariant Derivatives @DietterichLabs

Uploaded October 2018 | Updated September 2026, 3 days ago

In this video, I show you how to use standard covariant derivatives to derive the expressions for the standard divergence and gradient in spherical coordinates.

Superfluid Helium Resonance Experiment video:
youtu.be/unUNQNmuvUQ

Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou

There is a minus sign on the Christoffel term in the first expressions for the divergence. This is a typo. It should be a plus sign because it is the covariant derivative of a contravariant vector. This formula was not used in any of the calculations. The orthonormal basis expression used in the actual calculation has the correct sign, so all of the calculations are unaffected.

The Divergence And Gradient In Spherical Coordinates From Covariant Derivatives

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