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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.

Conformal mapping. --- Conformal representation of surfaces --- Mapping, Conformal --- Transformation, Conformal --- Geometric function theory --- Mappings (Mathematics) --- Surfaces, Representation of --- Transformations (Mathematics) --- Schwarz-Christoffel transformation --- 517.54 --- 517.95 --- 517.95 Partial differential equations --- Partial differential equations --- 517.54 Conformal mapping and geometric problems in the theory of functions of a complex variable. Analytic functions and their generalizations --- Conformal mapping and geometric problems in the theory of functions of a complex variable. Analytic functions and their generalizations --- S-C transformation --- Schwarz-Christoffel formula --- Schwarz-Christoffel mapping --- Conformal mapping --- Schwarz-Christoffel transformation. --- Applications conformes --- Numerical analysis

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First published in 1963, in East Germany, They Divided the Sky tells the story of a young couple, living in the new, socialist, East Germany, whose relationship is tested to the extreme not only because of the political positions they gradually develop but, very concretely, by the Berlin Wall, which went up on August 13, 1961.

Conformal invariants. --- Quantum field theory. --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Conformal invariance --- Invariants, Conformal --- Conformal mapping --- Functions of complex variables

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This book, part of the series Contributions in Mathematical and Computational Sciences, reviews recent developments in the theory of vertex operator algebras (VOAs) and their applications to mathematics and physics.   The mathematical theory of VOAs originated from the famous monstrous moonshine conjectures of J.H. Conway and S.P. Norton, which predicted a deep relationship between the characters of the largest simple finite sporadic group, the Monster, and the theory of modular forms inspired by the observations of J. MacKay and J. Thompson.   The contributions are based on lectures delivered at the 2011 conference on Conformal Field Theory, Automorphic Forms and Related Topics, organized by the editors as part of a special program offered at Heidelberg University that summer under the sponsorship of the MAThematics Center Heidelberg (MATCH).

Conformal invariants. --- Automorphic forms. --- Mathematics. --- Math --- Science --- Automorphic functions --- Forms (Mathematics) --- Conformal invariance --- Invariants, Conformal --- Conformal mapping --- Functions of complex variables --- Number theory. --- Mathematical physics. --- Number Theory. --- Mathematical Methods in Physics. --- Physical mathematics --- Physics --- Number study --- Numbers, Theory of --- Algebra --- Mathematics --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

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This book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2). There are many ways to develop this theory as the literature shows. The authors' approach is based on the use of metrics, in particular conformally invariant metrics, which will have a key role throughout the whole book. The intended readership consists of mathematicians from beginning graduate students to researchers. The prerequisite requirements are modest: only some familiarity with basic ideas of real and complex analysis is expected.

Potential theory (Mathematics). --- Differential geometry. --- Potential Theory. --- Differential Geometry. --- Differential geometry --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Quasiconformal mappings. --- Mappings, Quasiconformal --- Conformal mapping --- Functions of complex variables --- Geometric function theory --- Mappings (Mathematics)

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This textbook accounts for two seemingly unrelated mathematical topics drawn from two separate areas of mathematics that have no evident points of contiguity. Green's function is a topic in partial differential equations and covered in most standard texts, while infinite products are used in mathematical analysis. For the two-dimensional Laplace equation, Green's functions are conventionally constructed by either the method of images, conformal mapping, or the eigenfunction expansion. The present text focuses on the construction of Green's functions for a wide range of boundary-value problems. Green's Functions and Infinite Products provides a thorough introduction to the classical subjects of the construction of Green's functions for the two-dimensional Laplace equation and the infinite product representation of elementary functions.  Every chapter begins with a review guide, outlining the basic concepts covered. A set of carefully designed challenging exercises is available at the end of each chapter to provide the reader with the opportunity to explore the concepts in more detail. Hints, comments, and answers to most of those exercises can be found at the end of the text. In addition, several illustrative examples are offered at the end of most sections. This text is intended for an elective graduate course or seminar within the scope of either pure or applied mathematics.

Green's functions --- Products, Infinite --- Conformal mapping --- Eigenfunction expansions --- Engineering & Applied Sciences --- Physics --- Physical Sciences & Mathematics --- Applied Mathematics --- Atomic Physics --- Green's functions. --- Products, Infinite. --- Infinite products --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Differential equations. --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Analysis. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Applications of Mathematics. --- Algebra --- Processes, Infinite --- Differential equations --- Potential theory (Mathematics) --- Global analysis (Mathematics). --- Differential Equations. --- Differential equations, partial. --- Math --- Science --- Partial differential equations --- 517.91 Differential equations --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Conformal mapping. --- Eigenfunction expansions. --- Engineering --- Engineering analysis --- Mathematical analysis --- 517.1 Mathematical analysis --- Mathematics --- classical Euler representations --- Hilbert's theorem --- method of images --- method of variation