Hi. I am a Mechanical Engineering student. I'm not good at complex variable theory and having problem with finding conformal mapping of a doubly connected region to an annulus (or vice versa).

I know that the annulus is bounded by two circles with inner radius **r** and outer radius **R** and the inner and outer radii are not independent and the ratio **R/r** must be determined uniqely by the doubly connected region.

My doubly connected region is actually a hollow shape in which the inner and outer boundaries are geometrically similar and concentric. Parametric shape functions of the inner and outer boundaries in **x-y** plane are expressed as: **{X=F(theta), Y=G(theta)}**.

I would be really thankful if you could help me over this issue or introduce to me some useful references.

B.G.B