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Synopsis
Computational Conformal Mapping provides a self-contained and systematic introduction to the theory and computation of conformal mappings of simply- or multiply-connected regions onto the unit disk or canonical regions. It provides a comprehensive and systematic coverage of the concepts and related numerical analysis with applications to different areas in applied math, physics and engineering. The style and presentation are readily accessible to graduates and researchers.
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About the Author
Prem Kishore Kythe has been Professor of Mathematics at University of New Orleans since 1974.
Review
"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
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- PublisherBirkhäuser
- Publication date1998
- ISBN 10 0817639969
- ISBN 13 9780817639969
- BindingHardcover
- LanguageEnglish
- Number of pages477
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Computational Conformal Mapping
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book evolved out of a graduate course given at the University of New Orleans in 1997. The class consisted of students from applied mathematics andengineering. Theyhadthebackgroundofatleastafirstcourseincomplex analysiswithemphasisonconformalmappingandSchwarz-Christoffeltrans formation, a firstcourse in numerical analysis, and good to excellent working knowledgeofMathematica withadditionalknowledgeofsomeprogramming languages. Sincetheclasshad nobackground inIntegralEquations, thechap tersinvolvingintegralequationformulations werenotcoveredindetail,except for Symm's integral equation which appealed to a subsetofstudents who had some training in boundary element methods. Mathematica was mostly used for computations. In fact, it simplified numerical integration and other oper ations very significantly, which would have otherwise involved programming inFortran, C, orotherlanguageofchoice, ifclassical numericalmethods were attempted. Overview Exact solutions of boundary value problems for simple regions, such as cir cles, squares or annuli, can be determined with relative ease even where the boundaryconditionsarerathercomplicated. Green'sfunctionsforsuchsimple regions are known. However, for regions with complex structure the solution ofa boundary value problem often becomes more difficult, even for a simple problemsuchastheDirichletproblem. Oneapproachtosolvingthesedifficult problems is to conformally transform a given multiply connected region onto Mathematica is a registered trade mark of Wolfram Research, Inc. ix x PREFACE simpler canonical regions. This will, however, result in change not only in the region and the associated boundary conditions but also in the governing differential equation. As compared to the simply connected regions, confor mal mapping ofmultiply connected regions suffers from severe limitations, one of which is the fact that equal connectivity ofregions is not a sufficient condition to effect a reciprocally connected map ofone region onto another. Seller Inventory # 9780817639969
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