Question

Discuss the divergence and slope of the curl. Support your response with not more than five mathematical proofs

Answer 1

Answer:

Prove divergence of curl is zero | the divergence of the curl of any vector field a is always zero.The stokes theorem gives the integral of the curl of a vector field on a surface in therms of the integral of the vector field on the boundary that encircles that surface. So, the divergence of the curl being zero means that the boundary has no boundary.

calculation:

For F:R3→R3 (confused?), the formulas for the divergence and curl of a vector field are divF=∂F1∂x+∂F2∂y+∂F3∂zcurlF=(∂F3∂y−∂F2∂z,∂F1∂z−∂F3∂x,∂F2∂x−∂F1∂y).

Hope it is helpful to you!!!!!!