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Computational Conformal Mapping (Hardcover, 1998 ed.)
Loot Price: R1,666
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Computational Conformal Mapping (Hardcover, 1998 ed.)
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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.
General
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