Computational Conformal Mapping

0. Introduction.- 1. Basic Concepts.- 2. Conformal Mappings.- 3. Schwarz—Christoffel Integrals.- 4. Polynomial Approximations.- 5. Nearly Circular Regions.- 6. Green’s Functions.- 7. Integral Equation Methods.- 8. Theodorsen’s Integral Equation.- 9. Symm’s Integral Equation.- 10. Airfoils.- 11. Doubly Connected Regions.- 12. Singularities.- 13. Multiply Connected Regions.- 14. Grid Generation.- Appendix A. Cauchy P. V. Integrals.- A.1. Numerical Evaluation.- Appendix B. Green’s Identities.- Appendix C. Riemann—Hilbert Problem.- C.1. Homogeneous Hilbert Problem.- C.2. Nonhomogeneous Hilbert Problem.- C.3. Riemann—Hilbert Problem.- Appendix D. Successive Approximations.- D.1. Tables.- Appendix E. Catalog of Conformal Mappings.- Bibliography 431 Notation.

"There are more than 75 case studies of concrete conformal maps and more than 95 end-of-chapter exercises... Accessible to graduate students...it can also serve as a handbook for scientists and engineers who want to work with conformal maps... The book is a welcome addition to the literature. Its ample supply of case studies of conformal maps between given domains and the end-of chapter exercises are particularly attractive and helpful."
--Mathematical Reviews