Contents of postings on Conformal Mapping

1. Introduction and application of the conformal mapping z^0.5 to fluid flow.
   • Flash animation showing step-by-step distortion of images and coordinates by several conformal mappings.
   • Analysis of the transformation w = z^0.5.
   • Analysis of w = z².
   • Illustration of other flow patterns from the zⁿ transform.
   • More on incompressible, irrotational flow.
   
   
2. Conformal Mapping II.
   • More on analytic functions.
   • Derivation of the Cauchy-Riemann equations.
   • Graphical interpretation of the Cauchy-Riemann equations.
   • Comparison of complex derivatives with derivatives in a normal two dimensional space.
   • 2D versus 3D space using conformal mapping.
   • More on Laplace's equation boundary conditions and the uniqueness theorem.
   • Examples of picking an analytic function suitable for a particular fluid flow problem.
   
   
3. Fluid flow patterns handled by other functions.
   • The function w = e^z.
   • The function w = sinz.
   • The function w = z + 1/z.
   
   
4. Conformal mapping of electric and magnetic fields.
   • Starting electric and magnetic potentials and their fields.
   • A case of matching potentials at the boundaries.
   • Boundary conditions in electric fields.
   • Boundary conditions in magnetic fields.
   • Laplace's equation applied to resistive flow of charge and fluid.
   • Laplace's equation applied to time varying electric and magnetic fields.
   
   
5. Detailed conformal mappings.
   • Introduction.
   • w = z^0.5
   • w = z^1.5
   • w = z²
   • w = e^z
   • w = sinz
   • w = sinz, another domain.
   • w = tanz
   • w = z + 1/z
   • w = 1/z
   • Shifting and scaling
   • Overview of conformal mapping.
   • Links to more material on conformal mapping on the web.
   
   
6. Listing of all physics postings by the author.