Download or read book A Conformal Mapping Technique for Infinitely Connected Regions written by Maynard G. Arsove and published by American Mathematical Soc.. This book was released on 1970 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods of classical analysis devised originally for the disc are here extended to more general plane regions by the use of Green's lines, the Green's mapping, and an ideal boundary structure generalizing the prime-end structure of Carathéodory. The regions admitted include all bounded finitely connected regions, as well as a broad class of infinitely connected regions. Since certain modifications in the Brelot-Choquet theory are needed to allow for singular Green's lines, an independent development of the theory of Green's lines is given, based on properties of the Green's mapping. These techniques make possible the introduction of a generalized Poisson kernel and integral defined in terms of Green's lines.
Download or read book A Conformal Mapping Technique for Infinitely Connected Regions written by Maynard G. Arsove and published by American Mathematical Society(RI). This book was released on 1970-03 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Conformal Mapping written by Roland Schinzinger and published by Courier Corporation. This book was released on 2012-04-30 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beginning with a brief survey of some basic mathematical concepts, this graduate-level text proceeds to discussions of a selection of mapping functions, numerical methods and mathematical models, nonplanar fields and nonuniform media, static fields in electricity and magnetism, and transmission lines and waveguides. Other topics include vibrating membranes and acoustics, transverse vibrations and buckling of plates, stresses and strains in an elastic medium, steady state heat conduction in doubly connected regions, transient heat transfer in isotropic and anisotropic media, and fluid flow. Revision of 1991 ed. 247 figures. 38 tables. Appendices.
Download or read book Computational Conformal Mapping written by Prem Kythe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Conformal Mappings Onto Multiply Connected Regions with Specified Boundary Shapes A Preliminary Discussion of Computer Implementation written by Andrew Harrington and published by . This book was released on 1982 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author describes a method of calculating conformal mappings of any given finitely connected region onto a region with arbitrarily specified boundary shapes. If the specified shapes are rectangles, than this method can be used to generate conformal grids which should be useful for numerical solution of many partial differential equations, for example in calculating the airflow past an airflow with flaps or the flow of cooling water past fuel pins in a nuclear reactor. He has proved that there exists a conformal mapping of any given finitely connected region onto a region with arbitrarily specified boundary shapes. The construction in the proof has been adapted for computer implementation. Some examples have been worked to determine the region bounded by circles which is the image of a given region in the extended complex plane under a conformal mapping taking infinity to infinity. A region whose outer boundary is a rectangle is mapped conformally to a region with all rectangular boundaries, and the vertices of the outer boundaries correspond. Mappings onto regions bounded by rectangles should be of considerable use in grid generation for numerical solution of partial differential equations. Grids have been calculated for one simple example. (Author).
Download or read book Handbook of Conformal Mappings and Applications written by Prem K. Kythe and published by CRC Press. This book was released on 2019-03-04 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of conformal mappings is a major part of geometric function theory that gained prominence after the publication of the Riemann mapping theorem — for every simply connected domain of the extended complex plane there is a univalent and meromorphic function that maps such a domain conformally onto the unit disk. The Handbook of Conformal Mappings and Applications is a compendium of at least all known conformal maps to date, with diagrams and description, and all possible applications in different scientific disciplines, such as: fluid flows, heat transfer, acoustics, electromagnetic fields as static fields in electricity and magnetism, various mathematical models and methods, including solutions of certain integral equations.
Download or read book Rapid Methods for the Conformal Mapping of Multiply Connected Regions written by International Business Machines Corporation. Research Division and published by . This book was released on 1985 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Canonical Conformal Maps of Multiply Connected Regions written by Joseph Leonard Walsh and published by . This book was released on 1958 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Conformal Mapping of Simply Connected Regions written by Maxwell Duncan McCornock and published by . This book was released on 1967 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Schwarz Christoffel Mapping written by Tobin A. Driscoll and published by Cambridge University Press. This book was released on 2002-06-20 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, 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.
Download or read book Handbook of Conformal Mappings and Applications written by Prem K. Kythe and published by CRC Press. This book was released on 2019-03-04 with total page 943 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of conformal mappings is a major part of geometric function theory that gained prominence after the publication of the Riemann mapping theorem — for every simply connected domain of the extended complex plane there is a univalent and meromorphic function that maps such a domain conformally onto the unit disk. The Handbook of Conformal Mappings and Applications is a compendium of at least all known conformal maps to date, with diagrams and description, and all possible applications in different scientific disciplines, such as: fluid flows, heat transfer, acoustics, electromagnetic fields as static fields in electricity and magnetism, various mathematical models and methods, including solutions of certain integral equations.
Download or read book NASA Technical Translation written by and published by . This book was released on 1970 with total page 1026 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Conformal Mapping of Simply Connected Regions written by Joseph Ross Brown and published by . This book was released on 1949 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Conformal Mapping of Bounded Multiply Connected Regions by an Integral Equation Method written by Ali Hassan Mohamed Murid and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Construction and Applications of Conformal Maps written by Institute for Numerical Analysis (U.S.) and published by . This book was released on 1952 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Rapidly Converging Solution of the Conformal Mapping Problem of Hydrodynamics written by Leonard Pode and published by . This book was released on 1956 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Conformal Mapping written by Nicolas Papamichael and published by World Scientific. This book was released on 2010 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a unique monograph on numerical conformal mapping that gives a comprehensive account of the theoretical, computational and application aspects of the problems of determining conformal modules of quadrilaterals and of mapping conformally onto a rectangle. It contains a detailed study of the theory and application of a domain decomposition method for computing the modules and associated conformal mappings of elongated quadrilaterals, of the type that occur in engineering applications. The reader will find a highly useful and up-to-date survey of available numerical methods and associated computer software for conformal mapping. The book also highlights the crucial role that function theory plays in the development of numerical conformal mapping methods, and illustrates the theoretical insight that can be gained from the results of numerical experiments.This is a valuable resource for mathematicians, who are interested in numerical conformal mapping and wish to study some of the recent developments in the subject, and for engineers and scientists who use, or would like to use, conformal transformations and wish to find out more about the capabilities of modern numerical conformal mapping.
