It is straight forward to calculate the cross product of a function of 2 or 3 variables, but how can I calculate the curl of a function of 4 variables, for example:
F(t,x,y,z) = Bsin(ay - ωt)î?
2026-04-12 11:35:45.1775993745
∇×F (Curl) of a function of 4 variables?
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In general, extending the cross product (and therefore the curl) to more than three dimensions requires the machinery of differential forms. However, this is a special case, because it is generally understood that the curl (and gradient, divergence, etc.) only operates on the spatial variables $x, y, z$. This means that as far as $\nabla \times$ is concerned, your function is a function of $x, y, z$ only, and $t$ is treated as a constant.