Integrals in the Complex Plane
In the previous chapter, we focused on the derivative of a function of a complex variable. In the present chapter, we establish the framework of integration in the complex plane. In particular, we study the powerful results of Cauchy for complex integrals, and their direct consequences. Further consequences follow in the next chapter, where we analyze the singularities of complex functions.
Line integral of a function w = f (z) = u (x,y) + iv (x,y) over a smooth curve C is defined as
which is reminiscent of line integral of a vector function. As in the case of vector functions, the definition can ...