What are the vivid examples of flux, divergence, circulation and curl in advanced mathematics?
If you have studied electromagnetism, there is a good analogy. For example, the electric flux is the number of electric field lines passing through a closed surface, the divergence is used to describe whether a point is a source or a leak (according to the Gauss theorem of electrostatic field, the source describes whether it is positive or negative), and the circulation can be understood as the ring integral of the electric field around a ring (of course, the electrostatic field is zero). If the circulation of a field is zero, then the field has no curl, for example, the electrostatic field has no curl. To sum up briefly, if the flux of a field is zero, there is no divergence (static magnetic field), and if the circulation of a field is zero, there is no curl (electrostatic field).