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If you keep in mind that a 0-form is a function and a 1-form is a row-vector field, all the familiar operations of vector calculus can be written in terms of the ones above. The gradient of a function f f is the 1-form df d f. The curl of a 1-form A A is the 1-form ⋆dA ⋆ d A. The divergence of a 1-form A A is the function ⋆d ⋆ A ⋆ d ...
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