Explorations in Complex Variables with Accompanying Applets

Chapter 4: Harmonic Univalent Mappings

Applets you may need to use for this chapter:

1. ComplexTool is used to plot the image of domains in C under complex-valued functions.
2. ShearTool is used to plot the image of domains in C under a complex-valued harmonic function that is formed by shearing an analytic function and its dilatation; the user enters the corresponding analytic function and dilatation without having to solve explicitly for the harmonic function.
3. LinComboTool is used to plot and explore the convex combination of complex-valued harmonic polygonal maps.