More Explorations in Complex Functions

The text begins with two introductory chapters to be used as a resource.  Chapters 3 and 4 are stand-alone introductions to complex dynamics and to univalent function theory, including deBrange's theorem, respectively.  Chapters 5--7 may be treated as a unit that leads from harmonic functions to covering surfaces to the uniformization theorem and Fuchsian groups.  Chapter 8 is a stand-alone treatment of quasiconformal mapping that paves the way for Chapter 9, an introduction to Teichmüller theory. The final chapters, 10-14, are largely stand-alone introductions to topics of both theoretical and applied interest: the Bergman kernel, theta functions and Jacobi inversion, Padé approximants and continued fractions, the Riemann--Hilbert problem and integral equations, and Darboux's method for computing asymptotics.