Advanced Engineering Mathematics, 7th Edition

20.4 Schwarz–Christoffel Transformations

INTRODUCTION

If D′ is a simply connected domain with at least one boundary point, then the famous Riemann mapping theorem asserts the existence of an analytic function g that conformally maps the unit open disk z < 1 onto D′. The Riemann mapping theorem is a pure existence theorem that does not specify a formula for the conformal mapping. Since the upper half-plane y > 0 can be conformally mapped onto this disk using a linear fractional transformation, it follows that there exists a conformal mapping