Schwarz-Christoffel MappingThis 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, as evidenced by the 76 figures based on quantitatively correct illustrative examples. There are over 150 classical and modern reference works cited for readers needing more details. There is also a brief appendix illustrating the use of the Schwarz-Christoffel Toolbox for MATLAB, a package for computation of these maps. |
Contents
Essentials of SchwarzChristoffel mapping | 9 |
Numerical methods | 23 |
Variations | 41 |
Applications | 75 |
Using the SC Toolbox | 115 |
Bibliography | 121 |
Index | 131 |
Common terms and phrases
A. R. Elcrat algorithm analytic annulus Appl applications approximation aspect ratio boundary conditions bounded solution Christoffel circular-arc polygons complex Comput conformal mapping conformal modulus conformal transformation corners CRDT cross-ratios crowding Delaunay triangulation determine Dirichlet values disk maps domain doubly connected Doubly connected regions embedding example exterior maps Faber polynomials gearlike regions geometry Green's function grid infinite integrand interior angles inverse iterations L-shaped L. N. Trefethen Laplace's equation Level curves linear Math MATLAB Möbius transformation Netlib numerical conformal mapping oblique derivative problem parameter problem Phys piecewise piecewise-constant polynomial prevertex prevertices quadrilateral real axis rectangle maps reflection Riemann mapping theorem Riemann surface SC formula SC integral SC map SC Toolbox Schwarz Schwarz-Christoffel formula Schwarz-Christoffel mapping Schwarz-Christoffel transformation SCPACK segments shown in Figure SIAM side lengths singularities slit strip map target region triangles unique unit circle upper half-plane vertex vertices w₁ Φι
Popular passages
Page 20 - Two generalized quadrilaterals are conformally equivalent if and only if they have the same modulus.
Page 5 - Dedekind as a professor of mathematics at the Swiss Federal Institute of Technology in Zurich. It was in Zurich that he published the first paper on the Schwarz-Christoffel formula, with the Italian title, "Sul problema delle temperature stazonarie e la rappresentazione di una data superficie
References to this book
Water Transport in Brick, Stone and Concrete Christopher Hall,William D. Hoff No preview available - 2002 |