i'm studying the book "Conformal Mapping: Method and Applications" from Schinzinger and more precisely the chapter 6 concerning non-planar field. In section 6.1.3 the author proposes to solve a cylindrical laplace equation by solving a cartesian laplace equation via a conformal mapping of the polar plane.
I've joined the concerned pages.
At one point he says $\phi(u,\zeta)$ (the potential in the cartesian coordinates) verifies the cylindrical laplace equation, which i think is wrong and if it really so, the whole demonstration fails.
can somebody verify this? It is of great concern since It is the only book to speek about those kind of mapping.