ABSTRACT
The transformations using the polynomials, and particularly the monomials of the form f(z) = (z − a) n , provide another important aspect of conformal mapping of a given domain D ⊂ ℂ in the z-plane onto a domain G ⊂ℂ in the w-plane. As mentioned in Chapter 3, the function w = f(z) does not always exist, and it may not be uniquely defined, since the Riemann mapping theorem guarantees the existence and uniqueness only under certain specific conditions. We will also discuss other transformations, like hyperbolas and Cassini’s ovals, mappings by exponential and logarithmic functions, trigonometric and hyperbolic functions, and certain cases of composite transformations.
