This book provides a comprehensive look at the Schwarz-Christoffel transformation, including its history and foundations, practical computation, common and less common variations, and many applications in fields such as electromagnetism, fluid flow, design and inverse problems, and the solution of linear systems of equations. It is an accessible resource for engineers, scientists, and applied mathematicians who seek more experience with theoretical or computational conformal mapping techniques. The most important theoretical results are stated and proved, but the emphasis throughout remains on concrete understanding and implementation. There is a brief appendix illustrating the use of the Schwarz-Christoffel Toolbox for MATLAB, the state-of-the-art package for computation of these maps.
Preface; 1. Introduction; 2. Essentials; 3. Numerical methods; 4. Variations; 5. Applications; Using the SC toolbox.
"This is a very welcome addition to the literature of Schwarz-Christoffel (SC) transformations and, more generally, to the constructive conformal mapping literature.... The book is very well written and extremely informative. In particular, it reports on all the recent algorithmic developments and gives a clear picture of the remarkable capabilities of modern SC mapping.... Another attractive feature of the book is that most of its 76 figures are computer-generated (using the SC Toolbox) and are not just schematic but also quantitatively correct.... This is a very nice book. I recommend it, enthusiastically, to all those who work in numerical conformal mapping, to those who wish to find out about the modern capabilities of constructive SC mapping, and to all the engineering and science practitioners who might wish to use conformal mapping in applications but are not aware of these capabilities." Mathematical Reviews Mathematical Reviews