Pólya Vector Fields and Complex Integration along Closed Curves
Pólya Vector Fields and Complex Integration along Closed Curves
The Pólya vector field for a complex-valued function is the vector field . This field is displayed along a curve, allowing for a visual interpretation of the complex integral. The real part of the complex integral is the same as the integral of the tangential flow, while the imaginary part is given by the integral of the normal flow.
u(x,y)+iv(x,y)
〈u(x,y),-v(x,y)〉