Today we derive the expression for curl in a general covariant notation. We do this by promoting vectors to covariant vectors, derivatives to covariant derivatives, and also promote the levi-civita symbol to an actual tensor.
This series is based off "Tensor Calculus for Physics" by Dwight Neuenschwander which can be found at:
https://www.amazon.com/gp/product/142...
Levi_Civita Transformation Rule (See pg's 11-12)
http://bohr.physics.berkeley.edu/clas...
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Video relating Jacobians to the metric (Ep. 8 ~ 32 minutes in):
• Tensor Calculus For Physics Ep 8| The...