Advertisement
| application of conformal mapping: Conformal Mapping Roland Schinzinger, Patricio A. A. Laura, 2012-04-30 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. |
| application of conformal mapping: Handbook of Conformal Mappings and Applications Prem K. Kythe, 2019-03-04 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. |
| application of conformal mapping: Conformal Mapping Zeev Nehari, 2012-05-23 Conformal mapping is a field in which pure and applied mathematics are both involved. This book tries to bridge the gulf that many times divides these two disciplines by combining the theoretical and practical approaches to the subject. It will interest the pure mathematician, engineer, physicist, and applied mathematician. The potential theory and complex function theory necessary for a full treatment of conformal mapping are developed in the first four chapters, so the reader needs no other text on complex variables. These chapters cover harmonic functions, analytic functions, the complex integral calculus, and families of analytic functions. Included here are discussions of Green's formula, the Poisson formula, the Cauchy-Riemann equations, Cauchy's theorem, the Laurent series, and the Residue theorem. The final three chapters consider in detail conformal mapping of simply-connected domains, mapping properties of special functions, and conformal mapping of multiply-connected domains. The coverage here includes such topics as the Schwarz lemma, the Riemann mapping theorem, the Schwarz-Christoffel formula, univalent functions, the kernel function, elliptic functions, univalent functions, the kernel function, elliptic functions, the Schwarzian s-functions, canonical domains, and bounded functions. There are many problems and exercises, making the book useful for both self-study and classroom use. The author, former professor of mathematics at Carnegie-Mellon University, has designed the book as a semester's introduction to functions of a complex variable followed by a one-year graduate course in conformal mapping. The material is presented simply and clearly, and the only prerequisite is a good working knowledge of advanced calculus. |
| application of conformal mapping: Boundary Behaviour of Conformal Maps Christian Pommerenke, 2013-04-09 We study the boundary behaviour of a conformal map of the unit disk onto an arbitrary simply connected plane domain. A principal aim of the theory is to obtain a one-to-one correspondence between analytic properties of the function and geometrie properties of the domain. In the classical applications of conformal mapping, the domain is bounded by a piecewise smooth curve. In many recent applications however, the domain has a very bad boundary. It may have nowhere a tangent as is the case for Julia sets. Then the conformal map has many unexpected properties, for instance almost all the boundary is mapped onto almost nothing and vice versa. The book is meant for two groups of users. (1) Graduate students and others who, at various levels, want to learn about conformal mapping. Most sections contain exercises to test the understand ing. They tend to be fairly simple and only a few contain new material. Pre requisites are general real and complex analyis including the basic facts about conformal mapping (e.g. AhI66a). (2) Non-experts who want to get an idea of a particular aspect of confor mal mapping in order to find something useful for their work. Most chapters therefore begin with an overview that states some key results avoiding tech nicalities. The book is not meant as an exhaustive survey of conformal mapping. Several important aspects had to be omitted, e.g. numerical methods (see e.g. |
| application of conformal mapping: Handbook of Conformal Mapping with Computer-Aided Visualization Valentin I. Ivanov, Michael K. Trubetskov, 1994-12-16 This book is a guide on conformal mappings, their applications in physics and technology, and their computer-aided visualization. Conformal mapping (CM) is a classical part of complex analysis having numerous applications to mathematical physics. This modern handbook on CM includes recent results such as the classification of all triangles and quadrangles that can be mapped by elementary functions, mappings realized by elliptic integrals and Jacobian elliptic functions, and mappings of doubly connected domains. This handbook considers a wide array of applications, among which are the construction of a Green function for various boundary-value problems, streaming around airfoils, the impact of a cylinder on the surface of a liquid, and filtration under a dam. With more than 160 domains included in the catalog of mapping, Handbook of Conformal Mapping with Computer-Aided Visualization is more complete and useful than any previous volume covering this important topic. The authors have developed an interactive ready-to-use software program for constructing conformal mappings and visualizing plane harmonic vector fields. The book includes a floppy disk for IBM-compatible computers that contains the CONFORM program. |
| application of conformal mapping: Applied Complex Variables for Scientists and Engineers Yue Kuen Kwok, 2010-06-24 This introduction to complex variable methods begins by carefully defining complex numbers and analytic functions, and proceeds to give accounts of complex integration, Taylor series, singularities, residues and mappings. Both algebraic and geometric tools are employed to provide the greatest understanding, with many diagrams illustrating the concepts introduced. The emphasis is laid on understanding the use of methods, rather than on rigorous proofs. Throughout the text, many of the important theoretical results in complex function theory are followed by relevant and vivid examples in physical sciences. This second edition now contains 350 stimulating exercises of high quality, with solutions given to many of them. Material has been updated and additional proofs on some of the important theorems in complex function theory are now included, e.g. the Weierstrass–Casorati theorem. The book is highly suitable for students wishing to learn the elements of complex analysis in an applied context. |
| application of conformal mapping: Numerical Conformal Mapping Nicolas Papamichael, Nikos Stylianopoulos, 2010 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. |
| application of conformal mapping: Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces Richard Courant, 2005-01-01 Originally published: New York: Interscience Publishers, 1950, in series: Pure and applied mathematics (Interscience Publishers); v. 3. |
| application of conformal mapping: Inversion Theory and Conformal Mapping David E. Blair, 2000-08-17 It is rarely taught in an undergraduate or even graduate curriculum that the only conformal maps in Euclidean space of dimension greater than two are those generated by similarities and inversions in spheres. This is in stark contrast to the wealth of conformal maps in the plane. The principal aim of this text is to give a treatment of this paucity of conformal maps in higher dimensions. The exposition includes both an analytic proof in general dimension and a differential-geometric proof in dimension three. For completeness, enough complex analysis is developed to prove the abundance of conformal maps in the plane. In addition, the book develops inversion theory as a subject, along with the auxiliary theme of circle-preserving maps. A particular feature is the inclusion of a paper by Caratheodory with the remarkable result that any circle-preserving transformation is necessarily a Mobius transformation, not even the continuity of the transformation is assumed. The text is at the level of advanced undergraduates and is suitable for a capstone course, topics course, senior seminar or independent study. Students and readers with university courses in differential geometry or complex analysis bring with them background to build on, but such courses are not essential prerequisites. |
| application of conformal mapping: Applied and Computational Complex Analysis, Volume 1 Peter Henrici, 1988-02-23 Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions. |
| application of conformal mapping: The Kernel Function and Conformal Mapping Stefan Bergman, 1950-03 The Kernel Function and Conformal Mapping by Stefan Bergman is a revised edition of The Kernel Function. The author has made extensive changes in the original volume. The present book will be of interest not only to mathematicians, but also to engineers, physicists, and computer scientists. The applications of orthogonal functions in solving boundary value problems and conformal mappings onto canonical domains are discussed; and publications are indicated where programs for carrying out numerical work using high-speed computers can be found.The unification of methods in the theory of functions of one and several complex variables is one of the purposes of introducing the kernel function and the domains with a distinguished boundary. This approach has been extensively developed during the last two decades. This second edition of Professor Bergman's book reviews this branch of the theory including recent developments not dealt with in the first edition. The presentation of the topics is simple and presupposes only knowledge of an elementary course in the theory of analytic functions of one variable. |
| application of conformal mapping: Univalent Functions and Conformal Mapping James A. Jenkins, 2012-12-06 This monograph deals with the application of the method of the extremal metric to the theory of univalent functions. Apart from an introductory chapter in which a brief survey of the development of this theory is given there is therefore no attempt to follow up other methods of treatment. Nevertheless such is the power of the present method that it is possible to include the great majority of known results on univalent functions. It should be mentioned also that the discussion of the method of the extremal metric is directed toward its application to univalent functions, there being no space to present its numerous other applications, particularly to questions of quasiconformal mapping. Also it should be said that there has been no attempt to provide an exhaustive biblio graphy, reference normally being confined to those sources actually quoted in the text. The central theme of our work is the General Coefficient Theorem which contains as special cases a great many of the known results on univalent functions. In a final chapter we give also a number of appli cations of the method of symmetrization. At the time of writing of this monograph the author has been re ceiving support from the National Science Foundation for which he wishes to express his gratitude. His thanks are due also to Sister BARBARA ANN Foos for the use of notes taken at the author's lectures in Geo metric Function Theory at the University of Notre Dame in 1955-1956. |
| application of conformal mapping: Handbook of Conformal Mappings and Applications Prem K. Kythe, 2019-03-04 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. |
| application of conformal mapping: The Cauchy Transform, Potential Theory and Conformal Mapping Steven R. Bell, 2015-11-04 The Cauchy Transform, Potential Theory and Conformal Mapping explores the most central result in all of classical function theory, the Cauchy integral formula, in a new and novel way based on an advance made by Kerzman and Stein in 1976.The book provides a fast track to understanding the Riemann Mapping Theorem. The Dirichlet and Neumann problems f |
| application of conformal mapping: Computational Conformal Mapping Prem Kythe, 1998-12-08 A textbook for a graduate class or for self-study by students of applied mathematics and engineering. Assumes at least a first course in complex analysis with emphasis on conformal mapping and Schwarz- Christoffel transformation, a first course in numerical analysis, a solid working competence with the Mathematica software, and some additional knowledge of programming languages. Introduces the theory and computation of conformal mappings of regions that are connected, simply or multiply, onto the unit disk or canonical regions in order to solve boundary value problems. Annotation copyrighted by Book News, Inc., Portland, OR |
| application of conformal mapping: Moduli of Families of Curves for Conformal and Quasiconformal Mappings Alexander Vasilʹev, 2002-07-23 The monograph is concerned with the modulus of families of curves on Riemann surfaces and its applications to extremal problems for conformal, quasiconformal mappings, and the extension of the modulus onto Teichmller spaces. The main part of the monograph deals with extremal problems for compact classes of univalent conformal and quasiconformal mappings. Many of them are grouped around two-point distortion theorems. Montel's functions and functions with fixed angular derivatives are also considered. The last portion of problems is directed to the extension of the modulus varying the complex structure of the underlying Riemann surface that sheds some new light on the metric problems of Teichmller spaces. |
| application of conformal mapping: Conformal Maps And Geometry Dmitry Beliaev, 2019-11-19 'I very much enjoyed reading this book … Each chapter comes with well thought-out exercises, solutions to which are given at the end of the chapter. Conformal Maps and Geometry presents key topics in geometric function theory and the theory of univalent functions, and also prepares the reader to progress to study the SLE. It succeeds admirably on both counts.'MathSciNetGeometric function theory is one of the most interesting parts of complex analysis, an area that has become increasingly relevant as a key feature in the theory of Schramm-Loewner evolution.Though Riemann mapping theorem is frequently explored, there are few texts that discuss general theory of univalent maps, conformal invariants, and Loewner evolution. This textbook provides an accessible foundation of the theory of conformal maps and their connections with geometry.It offers a unique view of the field, as it is one of the first to discuss general theory of univalent maps at a graduate level, while introducing more complex theories of conformal invariants and extremal lengths. Conformal Maps and Geometry is an ideal resource for graduate courses in Complex Analysis or as an analytic prerequisite to study the theory of Schramm-Loewner evolution. |
| application of conformal mapping: Complex Variables with Applications Saminathan Ponnusamy, Herb Silverman, 2007-05-26 Explores the interrelations between real and complex numbers by adopting both generalization and specialization methods to move between them, while simultaneously examining their analytic and geometric characteristics Engaging exposition with discussions, remarks, questions, and exercises to motivate understanding and critical thinking skills Encludes numerous examples and applications relevant to science and engineering students |
| application of conformal mapping: Lectures on Quasiconformal Mappings Lars Valerian Ahlfors, 2006-07-14 Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of Teichmuller spaces, including the Bers embedding and the Teichmuller curve. It is remarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmuller spaces from these lecture notes. This edition includes three new chapters. The first, written by Earle and Kra, describes further developments in the theory of Teichmuller spaces and provides many references to the vast literature on Teichmuller spaces and quasiconformal mappings. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. The third, by Hubbard, illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3-manifolds. Together, these three new chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings. |
| application of conformal mapping: Conformal Representation Constantin Caratheodory, 1998-01-01 Comprehensive introduction discusses the Möbius transformation, non-Euclidean geometry, elementary transformations, Schwarz's Lemma, transformation of the frontier and closed surfaces, and the general theorem of uniformization. Detailed proofs. |
| application of conformal mapping: Complex Analysis with Applications in Science and Engineering Harold Cohen, 2010-04-23 The Second Edition of this acclaimed text helps you apply theory to real-world applications in mathematics, physics, and engineering. It easily guides you through complex analysis with its excellent coverage of topics such as series, residues, and the evaluation of integrals; multi-valued functions; conformal mapping; dispersion relations; and analytic continuation. Worked examples plus a large number of assigned problems help you understand how to apply complex concepts and build your own skills by putting them into practice. This edition features many new problems, revised sections, and an entirely new chapter on analytic continuation. |
| application of conformal mapping: Complex Analysis and Applications Hemant Kumar Pathak, 2019-08-19 This book offers an essential textbook on complex analysis. After introducing the theory of complex analysis, it places special emphasis on the importance of Poincare theorem and Hartog’s theorem in the function theory of several complex variables. Further, it lays the groundwork for future study in analysis, linear algebra, numerical analysis, geometry, number theory, physics (including hydrodynamics and thermodynamics), and electrical engineering. To benefit most from the book, students should have some prior knowledge of complex numbers. However, the essential prerequisites are quite minimal, and include basic calculus with some knowledge of partial derivatives, definite integrals, and topics in advanced calculus such as Leibniz’s rule for differentiating under the integral sign and to some extent analysis of infinite series. The book offers a valuable asset for undergraduate and graduate students of mathematics and engineering, as well as students with no background in topological properties. |
| application of conformal mapping: Conformal Geometry Miao Jin, Xianfeng Gu, Ying He, Yalin Wang, 2018-04-10 This book offers an essential overview of computational conformal geometry applied to fundamental problems in specific engineering fields. It introduces readers to conformal geometry theory and discusses implementation issues from an engineering perspective. The respective chapters explore fundamental problems in specific fields of application, and detail how computational conformal geometric methods can be used to solve them in a theoretically elegant and computationally efficient way. The fields covered include computer graphics, computer vision, geometric modeling, medical imaging, and wireless sensor networks. Each chapter concludes with a summary of the material covered and suggestions for further reading, and numerous illustrations and computational algorithms complement the text. The book draws on courses given by the authors at the University of Louisiana at Lafayette, the State University of New York at Stony Brook, and Tsinghua University, and will be of interest to senior undergraduates, graduates and researchers in computer science, applied mathematics, and engineering. |
| application of conformal mapping: Complex Analysis Andrei Bourchtein, Ludmila Bourchtein, 2021-02-09 This book discusses all the major topics of complex analysis, beginning with the properties of complex numbers and ending with the proofs of the fundamental principles of conformal mappings. Topics covered in the book include the study of holomorphic and analytic functions, classification of singular points and the Laurent series expansion, theory of residues and their application to evaluation of integrals, systematic study of elementary functions, analysis of conformal mappings and their applications—making this book self-sufficient and the reader independent of any other texts on complex variables. The book is aimed at the advanced undergraduate students of mathematics and engineering, as well as those interested in studying complex analysis with a good working knowledge of advanced calculus. The mathematical level of the exposition corresponds to advanced undergraduate courses of mathematical analysis and first graduate introduction to the discipline. The book contains a large number of problems and exercises, making it suitable for both classroom use and self-study. Many standard exercises are included in each section to develop basic skills and test the understanding of concepts. Other problems are more theoretically oriented and illustrate intricate points of the theory. Many additional problems are proposed as homework tasks whose level ranges from straightforward, but not overly simple, exercises to problems of considerable difficulty but of comparable interest. |
| application of conformal mapping: Computational Conformal Geometry Xianfeng David Gu, Shing-Tung Yau, 2008 |
| application of conformal mapping: Complex Analysis Joseph Bak, Donald J. Newman, 2010-08-02 This unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variable calculus and topology, the text focuses on the authentic complex-variable ideas and techniques. Accessible to students at their early stages of mathematical study, this full first year course in complex analysis offers new and interesting motivations for classical results and introduces related topics stressing motivation and technique. Numerous illustrations, examples, and now 300 exercises, enrich the text. Students who master this textbook will emerge with an excellent grounding in complex analysis, and a solid understanding of its wide applicability. |
| application of conformal mapping: Schwarz-Christoffel Mapping Tobin Allen Driscoll, Lloyd Nicholas Trefethen, 2002 This book provides a comprehensive look at the Schwarz-Christoffel transformation, including its history and foundations, practical computation, common and less common variations, and its many applications. It is intended as an accessible resource for engineers, scientists, and applied mathematicians who may not have much prior experience with theoretical or computational conformal mapping techniques. |
| application of conformal mapping: Fundamentals and Applications of Complex Analysis Harold Cohen, 2003-07-31 This book is intended to serve as a text for first and second year courses in single variable complex analysis. The material that is appropriate for more advanced study is developed from elementary material. The concepts are illustrated with large numbers of examples, many of which involve problems students encounter in other courses. For example, students who have taken an introductory physics course will have encountered analysis of simple AC circuits. This text revisits such analysis using complex numbers. Cauchy's residue theorem is used to evaluate many types of definite integrals that students are introduced to in the beginning calculus sequence. Methods of conformal mapping are used to solve problems in electrostatics. The book contains material that is not considered in other popular complex analysis texts. |
| application of conformal mapping: Conformal Projections in Geodesy and Cartography Paul D. Thomas, 1952 The purpose of this publication is to bring together in one volume and to give in detail the mathematical development of the formulas (or source references) for these projections in their various forms for the convenience of the geodetic computers and cartographers of the Coast and Geodetic Survey. It will supersede Special Publication No. 53, since it will incorporate the essential material contained therein.--Page iii. |
| application of conformal mapping: Complex Variables Steven G. Krantz, 2007-09-19 From the algebraic properties of a complete number field, to the analytic properties imposed by the Cauchy integral formula, to the geometric qualities originating from conformality, Complex Variables: A Physical Approach with Applications and MATLAB explores all facets of this subject, with particular emphasis on using theory in practice. The first five chapters encompass the core material of the book. These chapters cover fundamental concepts, holomorphic and harmonic functions, Cauchy theory and its applications, and isolated singularities. Subsequent chapters discuss the argument principle, geometric theory, and conformal mapping, followed by a more advanced discussion of harmonic functions. The author also presents a detailed glimpse of how complex variables are used in the real world, with chapters on Fourier and Laplace transforms as well as partial differential equations and boundary value problems. The final chapter explores computer tools, including Mathematica®, MapleTM, and MATLAB®, that can be employed to study complex variables. Each chapter contains physical applications drawing from the areas of physics and engineering. Offering new directions for further learning, this text provides modern students with a powerful toolkit for future work in the mathematical sciences. |
| application of conformal mapping: Algorithmic Learning in a Random World Vladimir Vovk, Alexander Gammerman, Glenn Shafer, 2005-03-22 Algorithmic Learning in a Random World describes recent theoretical and experimental developments in building computable approximations to Kolmogorov's algorithmic notion of randomness. Based on these approximations, a new set of machine learning algorithms have been developed that can be used to make predictions and to estimate their confidence and credibility in high-dimensional spaces under the usual assumption that the data are independent and identically distributed (assumption of randomness). Another aim of this unique monograph is to outline some limits of predictions: The approach based on algorithmic theory of randomness allows for the proof of impossibility of prediction in certain situations. The book describes how several important machine learning problems, such as density estimation in high-dimensional spaces, cannot be solved if the only assumption is randomness. |
| application of conformal mapping: Translations of Mathematical Monographs , 1962 |
| application of conformal mapping: Map of the World Martin Vermeer, Antti Rasila, 2019-08-19 Carl Friedrich Gauss, the foremost of mathematicians, was a land surveyor. Measuring and calculating geodetic networks on the curved Earth was the inspiration for some of his greatest mathematical discoveries. This is just one example of how mathematics and geodesy, the science and art of measuring and mapping our world, have evolved together throughout history. This text is for students and professionals in geodesy, land surveying, and geospatial science who need to understand the mathematics of describing the Earth and capturing her in maps and geospatial data: the discipline known as mathematical geodesy. Map of the World: An Introduction to Mathematical Geodesy aims to provide an accessible introduction to this area, presenting and developing the mathematics relating to maps, mapping, and the production of geospatial data. Described are the theory and its fundamental concepts, its application for processing, analyzing, transforming, and projecting geospatial data, and how these are used in producing charts and atlases. Also touched upon are the multitude of cross-overs into other sciences sharing in the adventure of discovering what our world really looks like. FEATURES • Written in a fluid and accessible style, replete with exercises; adaptable for courses on different levels. • Suitable for students and professionals in the mapping sciences, but also for lovers of maps and map making. |
| application of conformal mapping: Visual Complex Analysis Tristan Needham, 1997 This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields. |
| application of conformal mapping: Map ProjectionsTheory and Applications Frederick Pearson, II, 1990-03-28 About the Author: Frederick Pearson has extensive experience in teaching map projection at the Air Force Cartography School and Virginia Polytechnic Institute. He developed star charts, satellite trajectory programs, and a celestial navigation device for the Aeronautical Chart and Information Center. He is an expert in orbital analysis of satellites, and control and guidance systems. At McDonnell-Douglas, he worked on the guidance system for the space shuttle. This text develops the plotting equations for the major map projections. The emphasis is on obtaining usable algorithms for computed aided plotting and CRT display. The problem of map projection is stated, and the basic terminology is introduced. The required fundamental mathematics is reviewed, and transformation theory is developed. Theories from differential geometry are particularized for the transformation from a sphere or spheroid as the model of the earth onto a selected plotting surface. The most current parameters to describe the figure of the earth are given. Formulas are included to calculate meridian length, parallel length, geodetic and geocentric latitude, azimuth, and distances on the sphere or spheroid. Equal area, conformal, and conventional projection transformations are derived. All result in direct transformation from geographic to cartesian coordinates. For selected projections, inverse transformations from cartesian to geographic coordinates are given. Since the avoidance of distortion is important, the theory of distortion is explored. Formulas are developed to give a quantitative estimate of linear, area, and angular distortions. Extended examples are given for several mapping problems of interest. Computer applications, and efficient algorithms are presented. This book is an appropriate text for a course in the mathematical aspects of mapping and cartography. Map projections are of interest to workers in many fields. Some of these are mathematicians, engineers, surveyors, geodicests, geographers, astronomers, and military intelligence analysts and strategists. |
| application of conformal mapping: Geometric Function Theory and Non-linear Analysis Tadeusz Iwaniec, Gaven Martin, 2001 Iwaniec (math, Syracuse U.) and Martin (math, U. of Auckland) explain recent developments in the geometry of mappings, related to functions or deformations between subsets of the Euclidean n-space Rn and more generally between manifolds or other geometric objects. Material on mappings intersects with aspects of differential geometry, topology, partial differential equations, harmonic analysis, and the calculus of variations. Chapters cover topics such as conformal mappings, stability of the Mobius group, Sobolev theory and function spaces, the Liouville theorem, even dimensions, Picard and Montel theorems in space, uniformly quasiregular mappings, and quasiconformal groups. c. Book News Inc. |
| application of conformal mapping: Complex Analysis and Applications Alan Jeffrey, 2005-11-10 Complex Analysis and Applications, Second Edition explains complex analysis for students of applied mathematics and engineering. Restructured and completely revised, this textbook first develops the theory of complex analysis, and then examines its geometrical interpretation and application to Dirichlet and Neumann boundary value problems. |
| application of conformal mapping: Complex Analysis and Applications William R. Derrick, 1984 |
| application of conformal mapping: Complex Analysis with Applications to Flows and Fields Luis Manuel Braga da Costa Campos, 2010-09-03 Complex Analysis with Applications to Flows and Fields presents the theory of functions of a complex variable, from the complex plane to the calculus of residues to power series to conformal mapping. The book explores numerous physical and engineering applications concerning potential flows, the gravity field, electro- and magnetostatics, steady he |
| application of conformal mapping: Computational Conformal Mapping Prem Kythe, 2012-12-06 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. |
Conformal Mapping and its Applications - IISER Pune
mapping it can be transferred to a problem with much more convenient geometry. This article gives a brief introduction to conformal mappings and some of its applications in physical problems.
Conformal Mapping - California Institute of Technology
Conformal Mapping. By utilizing the process of conformal mapping, we can substantially enhance our ability to find solutions to planar potential flows by the method of complex variables. In its simplest form the process involves taking.
Notes on Conformal Mappings and The Riemann Mapping …
Conformal Mappings To return to the problem at hand, it is usually recommended to proceed in two steps. Suppose we are given two nice regions ; ˆC and which to nd a conformal mapping : !. In general, the best method is two nd two auxiliary conformal mappings: !D; : D ! (4) so that := is a desired conformal mapping. 1{1.3 Automorphisms of D
Complex Analysis and Conformal Mapping - University of …
Conformal mappings can be effectively used for constructing solutions to the Laplace equation on complicated planar domains that appear in a wide range of physical problems, including fluid mechanics, aerodynamics, thermomechanics, electrostatics, and elasticity.
Conformal mapping - University of Minnesota Twin Cities
Paul Garrett: Conformal mapping (November 23, 2014) Three points on a circle determine the circle completely. A line in C can be viewed determined by two points on it in C, and inevitably passing through 1. The group of linear fractional transformation actions
Lecture 2: Conformal mappings - Stanford University
The idea of a global conformal map is that we embed R(p,q) into a suitable completion or compactification, X, such that there is a sufficiently large collection of conformal automorphisms of X.
Lecture 20 Conformal mappings - GitHub Pages
A holomorphic function f: U!C is called a conformal map, if its derivative does not vanish. Example 4. Function f ( z ) = z 2 is a conformal mapping from Cf0gonto Cf0g.
Conformal Mapping in Wing Aerodynamics - University of …
The purpose of this exposition is to give the reader an elementary intro-duction to the use of conformal mapping in two-dimensional airfoil theory with ideal uids. Sections 2 and 3 will provide the reader with the prereq-uisite backround knowledge of basic airfoil theory and two-dimensional uid dynamics respectively.
Conformal mapping function of a complex domain and its application
In order to determine the stress–strain state for these or other problems of elasticity theory in such a complex domain, the function that maps the given domain S onto the exterior of a unique circle (or onto a half-plane) is determined first.
Cauchy-Riemann Equations and Conformal Mapping
Conformal Mapping 26.2 Introduction In this Section we consider two important features of complex functions. The Cauchy-Riemann equations provide a necessary and sufficient condition for a function f(z) to be analytic in some region of the complex plane; this allows us to find f0(z) in that region by the rules of the previous Section.
Conformal Mapping and its Applications - Universiti Teknologi …
Conformal Mapping • A mapping with the property that angles between curves are preserved in magnitude as well as in direction is called a conformal mapping. • Thus any set of orthogonal curves in the z-plane would therefore appear as another set of orthogonal curves in the w-plane. • Conformal mapping function can be found in the class of
Aero III/IV Conformal Mapping - University of Manchester
A conformal mapping is a mapping that preserves angle. More precisely, if w= f(z) is a conformal mapping, 1(t) and 2(t) are two curves on the z-plane intersect at t 0, then the angle (measured in terms of the tangent direction) between f(1(t)) and f(2(t)) is the same as that between 1(t) and 2(t). Example 2.1 (A conformal mapping from the rst ...
MA 201 Complex Analysis Lecture 18 and 19: Conformal Mapping …
MA 201 Complex Analysis Lecture 18 and 19: Conformal Mapping. Let S2 = f(x1; x2; x3) 2 R3 : x2. + x2. = 1g be the unit sphere R3 and let N = (0; 0; 1) denote the "north pole" of S2. Identify C with f(x1; x2; 0) : x1; x2 2 Rg so that C cuts S2 in the equator. For each z 2 C consider the straight line in R3 through z and N.
Genus Zero Surface Conformal Mapping and Its Application to …
In this paper, we propose a new genus zero surface conformal mapping algorithm [7] and demonstrate its use in computing conformal mappings between brain surfaces. Our algo-
Connections and conformal mapping - Project Euclid
theory of conformal mapping and Riemann surfaces. The present paper is devoted to an exposition of the role of connections in various applications of this kind.
CONFORMAL MAPPING, ITS TYPES AND APPLICATIONS - JETIR
Conformal mapping is an important technique used in complex analysis. A conformal mapping on Euclidean m-space Em can be decomposed into a product of similarity transformations and inversions.
Recent Advances at Stanford in the Application of Conformal Mapping …
RECENT ADVANCES AT STANFORD IN THE APPLICATION OF CONFORMAL MAPPING TO HYDRODYNAMICS P. R. GARABEDIAN, EDWARD McLEOD, JR., and MARTIN VITOUSEK, Stanford University The present paper forms an expository report of researches carried out re-cently at Stanford University by a group of mathematicians interested in free boundary …
Conformal mapping and its application to Laplace's equation
\conformal mapping" which can solve Laplace’s equation on more general domains. In this talk, we will look at two types of conformal mappings, namely, M obius transformation and Schwarz-Christo el transformation and discuss various examples illustrating the method.
Conformal Mapping and its Application to Laplace’s Equation
This project involves applying conformal mappings to solving Laplace’s equation. We assume the readers have sufficient knowledge in Laplace’s equations, Fourier series, Fourier transform and conformal mapping. For better understanding, please refer to Math 230 lecture notes
Conformal Mapping and its Application to Laplace's Equations
Laplace's equation is the PDE of the form. @2u @2u. + = 0; @x2 @y2. where u(x; y) is a real-valued function. A partial di erential equation (PDE) is a di erential equation involving partial derivatives with respect to more than one independent variable.
Conformal Mapping and its Applications - IISER Pune
mapping it can be transferred to a problem with much more convenient geometry. This article gives a brief introduction to conformal mappings and some of its applications in physical problems.
Conformal Mapping - California Institute of Technology
Conformal Mapping. By utilizing the process of conformal mapping, we can substantially enhance our ability to find solutions to planar potential flows by the method of complex variables. In its simplest form the process involves taking.
Notes on Conformal Mappings and The Riemann Mapping Theorem
Conformal Mappings To return to the problem at hand, it is usually recommended to proceed in two steps. Suppose we are given two nice regions ; ˆC and which to nd a conformal mapping : !. In general, the best method is two nd two auxiliary conformal mappings: !D; : D ! (4) so that := is a desired conformal mapping. 1{1.3 Automorphisms of D
Complex Analysis and Conformal Mapping - University of …
Conformal mappings can be effectively used for constructing solutions to the Laplace equation on complicated planar domains that appear in a wide range of physical problems, including fluid mechanics, aerodynamics, thermomechanics, electrostatics, and elasticity.
Conformal mapping - University of Minnesota Twin Cities
Paul Garrett: Conformal mapping (November 23, 2014) Three points on a circle determine the circle completely. A line in C can be viewed determined by two points on it in C, and inevitably passing through 1. The group of linear fractional transformation actions
Lecture 2: Conformal mappings - Stanford University
The idea of a global conformal map is that we embed R(p,q) into a suitable completion or compactification, X, such that there is a sufficiently large collection of conformal automorphisms of X.
Lecture 20 Conformal mappings - GitHub Pages
A holomorphic function f: U!C is called a conformal map, if its derivative does not vanish. Example 4. Function f ( z ) = z 2 is a conformal mapping from Cf0gonto Cf0g.
Conformal Mapping in Wing Aerodynamics - University of …
The purpose of this exposition is to give the reader an elementary intro-duction to the use of conformal mapping in two-dimensional airfoil theory with ideal uids. Sections 2 and 3 will provide the reader with the prereq-uisite backround knowledge of basic airfoil theory and two-dimensional uid dynamics respectively.
Conformal mapping function of a complex domain and its application
In order to determine the stress–strain state for these or other problems of elasticity theory in such a complex domain, the function that maps the given domain S onto the exterior of a unique circle (or onto a half-plane) is determined first.
Cauchy-Riemann Equations and Conformal Mapping
Conformal Mapping 26.2 Introduction In this Section we consider two important features of complex functions. The Cauchy-Riemann equations provide a necessary and sufficient condition for a function f(z) to be analytic in some region of the complex plane; this allows us to find f0(z) in that region by the rules of the previous Section.
Conformal Mapping and its Applications - Universiti Teknologi …
Conformal Mapping • A mapping with the property that angles between curves are preserved in magnitude as well as in direction is called a conformal mapping. • Thus any set of orthogonal curves in the z-plane would therefore appear as another set of orthogonal curves in the w-plane. • Conformal mapping function can be found in the class of
Aero III/IV Conformal Mapping - University of Manchester
A conformal mapping is a mapping that preserves angle. More precisely, if w= f(z) is a conformal mapping, 1(t) and 2(t) are two curves on the z-plane intersect at t 0, then the angle (measured in terms of the tangent direction) between f(1(t)) and f(2(t)) is the same as that between 1(t) and 2(t). Example 2.1 (A conformal mapping from the rst ...
MA 201 Complex Analysis Lecture 18 and 19: Conformal Mapping
MA 201 Complex Analysis Lecture 18 and 19: Conformal Mapping. Let S2 = f(x1; x2; x3) 2 R3 : x2. + x2. = 1g be the unit sphere R3 and let N = (0; 0; 1) denote the "north pole" of S2. Identify C with f(x1; x2; 0) : x1; x2 2 Rg so that C cuts S2 in the equator. For each z 2 C consider the straight line in R3 through z and N.
Genus Zero Surface Conformal Mapping and Its Application to …
In this paper, we propose a new genus zero surface conformal mapping algorithm [7] and demonstrate its use in computing conformal mappings between brain surfaces. Our algo-
Connections and conformal mapping - Project Euclid
theory of conformal mapping and Riemann surfaces. The present paper is devoted to an exposition of the role of connections in various applications of this kind.
CONFORMAL MAPPING, ITS TYPES AND APPLICATIONS - JETIR
Conformal mapping is an important technique used in complex analysis. A conformal mapping on Euclidean m-space Em can be decomposed into a product of similarity transformations and inversions.
Recent Advances at Stanford in the Application of Conformal Mapping …
RECENT ADVANCES AT STANFORD IN THE APPLICATION OF CONFORMAL MAPPING TO HYDRODYNAMICS P. R. GARABEDIAN, EDWARD McLEOD, JR., and MARTIN VITOUSEK, Stanford University The present paper forms an expository report of researches carried out re-cently at Stanford University by a group of mathematicians interested in free boundary problems of ...
Conformal mapping and its application to Laplace's equation
\conformal mapping" which can solve Laplace’s equation on more general domains. In this talk, we will look at two types of conformal mappings, namely, M obius transformation and Schwarz-Christo el transformation and discuss various examples illustrating the method.
Conformal Mapping and its Application to Laplace’s Equation
This project involves applying conformal mappings to solving Laplace’s equation. We assume the readers have sufficient knowledge in Laplace’s equations, Fourier series, Fourier transform and conformal mapping. For better understanding, please refer to Math 230 lecture notes
Conformal Mapping and its Application to Laplace's Equations
Laplace's equation is the PDE of the form. @2u @2u. + = 0; @x2 @y2. where u(x; y) is a real-valued function. A partial di erential equation (PDE) is a di erential equation involving partial derivatives with respect to more than one independent variable.
