complex line integral

The line integral of a vector field F(x) on a curve σ is defined by integral_σ F·d s = integral_a^b F(σ(t))·σ'(t) d t, where a·b denotes a dot product. In Cartesian coordinates, the line integral can be written integral_σ F·d s = integral_C F_1 d x + F_2 d y + F_3 d z, where F congruent [F_1(x) F_2(x) F_3(x)].

conservative field | contour integral | gradient theorem | irrotational field | path integral | Poincaré's theorem