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Vector-fields are vector valued functions which define a vector at each point in space. Examples of the vector field include the electric field and the velocity of a fluid.

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Replacing infinitesimals with full vectors in a differential relation. Is it legit?

I'm reading Leonard Susskind's "Special Relativity and Classical Field Theory". On pg. 138 he generalizes a differential relation by replacing infinitesimals with full vectors like so: Is this al …
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