sentences:  The theory of arbitrary airfoils based on conformal mapping developed by Theodorsen, is a model of classical applied mathematics.Two key concepts made Theodorsen’s approach different from and a clear improvement on the methods that preceded it, such as that of von Mises and von Karman.One was the important use of the complex variable not in the usual form of a polynomial or power series, but in the form of an exponential to power series.