Recall that a vector field F is conservative if there is a scalar-valued function f such that grad f=F. In this case, f is called a potential of F, and is only determined up to a constant.
The potential command computes the potential of a vector field, or signals an error if the vector field is not conservative.
Note that potential is the reciprocal function of derive.
Example.
Input:
Output:
x2 y+3 x−4 y z |
Note that in ℝ3, a vector field F is conservative if and only if its curl is zero; i.e., if curlF=0. In time-independent electro-magnetism, F=E is the electric field and f is the electric potential.