Key Equations
Vector field in | or |
Vector field in | or |
Calculating a scalar line integral | |
Calculating a vector line integral | or |
Calculating flux |
Fundamental Theorem for Line Integrals | |
Circulation of a conservative field over curve C that encloses a simply connected region |
Green’s theorem, circulation form | where C is the boundary of D |
Green’s theorem, flux form | where C is the boundary of D |
Green’s theorem, extended version |
Curl | |
Divergence | |
Divergence of curl is zero | |
Curl of a gradient is the zero vector |
Scalar surface integral | |
Flux integral |
Stokes’ theorem |
Divergence theorem |