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Driscoll T.A., Trefethen L.N. — Schwarz-Christoffel Mapping
Driscoll T.A., Trefethen L.N. — Schwarz-Christoffel Mapping

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Название: Schwarz-Christoffel Mapping

Авторы: Driscoll T.A., Trefethen L.N.

Аннотация:

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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 2002

Количество страниц: 132

Добавлена в каталог: 28.03.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$T_{E}X$      xv
Airplane window      15
Amplitwist      107
Analytic continuation      2 5 10 105 112 113
Approximation theory      xvi 108-111 114
Automatic control      76
Beta function, incomplete      18
Boundary correspondence      74 108
Branch cut      2 12 46 78
Brownian motion      97-99
Capacitance, electrical      76
Capacity      53 108 112
Carath$\acute{e}$odory - Osgood theorem      1
Cauchy - Riemann equations      107
Chebyshev polynomial      110
Christofifel, Elwin Bruno      4-6
Circular triangle      72
Circular-arc polygon      see “SC mapping”
Computers      4 6 23
Conformal center      12 77
Conformal modulus of quadrilateral      20 39 47-51 99-101
Conformalmodulus of doubly connected polygon      64 69 70
CONFPACK      39
Crack detection      76 100-101
CRDT algorithm      xvi 8 30-39
Cross-ratio      21 31
Crowding      xvi 7 20-21 23 25 28 30-31 43 44 45 47 72 78
Curved boundary      see “SC mapping”
Delaunay triangulation, xvi      32
Delaware      26
Digital filter      xvi 112 114
Domain decomposition      21 30-36
Doubly connected polygon      see “SC mapping”
Drum, can one hear shape of?      xv
DSCPACK      8 39 69-70
Electrical engineering      76
Elliptic integral      18-20 48-51 111
Elongated region      xv 7 21 30
Embedding      30
Extended complex plane      9 51 108
Exterior map      see “SC mapping”
Faber polynomial      108-111
Finite elements      xvi 28
Floating-point arithmetic      21 30
Fluid mechanics      57 76 101-105
Fractal      see “SC mapping”
Free-streamline flow      7 101-106
Gearlike domain      see “SC mapping”
Graphics      xv xvi 5 6 116
Green’s function      xvi 5 77 111-114
Hall effect      76 94 97
Harmonic function      87
Harmonic measure      114
Henrici, Peter      xv xvi
Hodograph variable      102
Hypergeometric function      72
Infinite vertex      see “Vertex at infinity”
Integral equation      28 74 76
Integrated circuit      76
Integration      see “Quadrature”
Inverse of SC map      4 29-30
Inverse problem      99-101
jet      76 105
Jordan region      19 60
Korteweg-de Vries equation      87
Krylov subspace method      111
Kufarev’s method      7 8
Laplace equation      75-99
Laplacian      107
Lightning      15
M$\ddot{o}$bius transformation      xvi 12 19 31-33 42 58-59 60 65 71 72 103
MATLAB      xv xvi 39 115-119
Matrix iteration      xvi 108-111
Maze      36-38
Mesh generation      37-39 76-77 105-108
Mesh refinement      xvi 28
Microwave waveguide      76
Multiply connected polygon      see “SC mapping”
NETLIB      39 72 105
Oblique derivative problem      xv 87-99
One-half rule      see “Quadrature”
Parameter problem      4 5 23-27 116
Parameter problem, generalized      7 99-101 112 114
Parameter problem, linear      85-87 94
Polygon      1 3 9-10
Porthole      15
Prevertices      1-4 23-27
Quadrature      4 7 27-29 116
Quadrature, compound Gauss - Jacobi      28-29
Quadrature, Gauss - Jacobi      28 105
Quadrature, Gauss - Legendre      105
Quadrature, Newton - Cotes      28
Quadrature, one-half rule for      xvi 28
Quadrilateral      5 32
Quadrilateral, generalized      19 48 99
rectangle      see “SC mapping”
Reentrant comer      15
Reflection      see “Schwarz reflection”
Resistance, electrical      47 76 99-101
Resistor trimming      76 99-101
Riemann mapping theorem      4 6 12 108
Riemann sphere      9 108
Riemann surface      see “SC mapping”
Rouch$\acute{e}$’s theorem      110
Roundoff error      see “Floating-point arithmetic”
Salient comer      15
SC mapping of circular-arc polygon      xvi 3 5 7 26 39 70-73
SC mapping of curved boundary region      5 7 26 73-74
SC mapping of disk      3 11-12 42-44 115
SC mapping of doubly connected polygon      xvi 3 7 8 39 64-70
SC mapping of exterior of polygon      3 5 51-54 115
SC mapping of fractal      55-57
SC mapping of gearlike region      7 39 60-63 115
SC mapping of half-plane      3 10-20 115
SC mapping of infinite stri      7 12-15 30 44-48
SC mapping of periodic polygon      7 55-57 58
SC mapping of rectangle      18-21 47-51
SC mapping of Riemann surface      58-61 80 86-87 115
SC mapping of symmetric multiply connected polygon      114
SC mapping of triangle      5 16-18
SC Toolbox      xv xvi 6 8 29 39 115-119
Schwarz - Christoffel      see “SC”
Schwarz Hermann Amandus      4-6
Schwarz reflection      2 10 13 57-58 65-68 70 113
Schwarzian      71 73
SCPACK      xv 6 7 39 111
Slit      1 3 9 14-15 17 26-27 30 45 69 83-87
Software      6 7 23 39-40 115-119
Strip      see “SC mapping”
Theta function      66 69
Transfinite diameter      see “Capacity”
triangle      see “SC mapping”
Turning angle      2
Van der Pauw resistor      76 87
Vertex at infinity      3 9 10 25 29
Wakes and cavities      76 101-106
Well-separated prevertices      33
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