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Symmetry And Separation Of Variables
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Book Synopsis Symmetry and Separation of Variables by : Willard Miller
Download or read book Symmetry and Separation of Variables written by Willard Miller and published by Cambridge University Press. This book was released on 2012-03-29 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1977, this volume is concerned with the relationship between symmetries of a linear second-order partial differential equation of mathematical physics, the coordinate systems in which the equation admits solutions via separation of variables, and the properties of the special functions that arise in this manner. Some group-theoretic twists in the ancient method of separation of variables that can be used to provide a foundation for much of special function theory are shown. In particular, it is shown explicitly that all special functions that arise via separation of variables in the equations of mathematical physics can be studied using group theory.
Book Synopsis Symmetry and Separation of Variables by : Willard Miller
Download or read book Symmetry and Separation of Variables written by Willard Miller and published by . This book was released on 2014-05-14 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1977 volume is concerned with the group-theoretic approach to special functions.
Book Synopsis Symmetry and Separation of Variables by : Glenn H. Leggett
Download or read book Symmetry and Separation of Variables written by Glenn H. Leggett and published by . This book was released on 1977 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Separation of Variables and Superintegrability by : E. G. Kalnins
Download or read book Separation of Variables and Superintegrability written by E. G. Kalnins and published by IOP Publishing Limited. This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Separation of variables methods for solving partial differential equations are of immense theoretical and practical importance in mathematical physics. They are the most powerful tool known for obtaining explicit solutions of the partial differential equations of mathematical physics. The purpose of this book is to give an up-to-date presentation of the theory of separation of variables and its relation to superintegrability. Collating and presenting in a unified, updated and a more accessible manner the results scattered in the literature the authors have prepared an invaluable resource for mathematicians and mathematical physicists in particular, as well as science, engineering, geological and biological researchers interested in explicit solutions.
Book Synopsis Separation of Variables and Exact Solutions to Nonlinear PDEs by : Andrei D. Polyanin
Download or read book Separation of Variables and Exact Solutions to Nonlinear PDEs written by Andrei D. Polyanin and published by CRC Press. This book was released on 2021-09-20 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Separation of Variables and Exact Solutions to Nonlinear PDEs is devoted to describing and applying methods of generalized and functional separation of variables used to find exact solutions of nonlinear partial differential equations (PDEs). It also presents the direct method of symmetry reductions and its more general version. In addition, the authors describe the differential constraint method, which generalizes many other exact methods. The presentation involves numerous examples of utilizing the methods to find exact solutions to specific nonlinear equations of mathematical physics. The equations of heat and mass transfer, wave theory, hydrodynamics, nonlinear optics, combustion theory, chemical technology, biology, and other disciplines are studied. Particular attention is paid to nonlinear equations of a reasonably general form that depend on one or several arbitrary functions. Such equations are the most difficult to analyze. Their exact solutions are of significant practical interest, as they are suitable to assess the accuracy of various approximate analytical and numerical methods. The book contains new material previously unpublished in monographs. It is intended for a broad audience of scientists, engineers, instructors, and students specializing in applied and computational mathematics, theoretical physics, mechanics, control theory, chemical engineering science, and other disciplines. Individual sections of the book and examples are suitable for lecture courses on partial differential equations, equations of mathematical physics, and methods of mathematical physics, for delivering special courses and for practical training.
Book Synopsis Separation of Variables and Superintegrability by : Willard Miller, Jr
Download or read book Separation of Variables and Superintegrability written by Willard Miller, Jr and published by . This book was released on 2018-06-13 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Separation of variables methods for solving partial differential equations are of immense theoretical and practical importance in mathematical physics. They are the most powerful tool known for obtaining explicit solutions of the partial differential equations of mathematical physics. The purpose of this book is to give an up-to-date presentation of the theory of separation of variables and its relation to superintegrability. Collating and presenting it in a unified, updated and a more accessible manner, the results scattered in the literature that the authors have prepared is an invaluable resource for mathematicians and mathematical physicists in particular, as well as science, engineering, geological and biological researchers interested in explicit solutions.
Book Synopsis Separation of Variables by the Symmetry Method for Second Order Linear Partial Differential Equations by : Leon Joseph Chandler
Download or read book Separation of Variables by the Symmetry Method for Second Order Linear Partial Differential Equations written by Leon Joseph Chandler and published by . This book was released on 1980 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Symmetry Methods for Differential Equations by : Peter Ellsworth Hydon
Download or read book Symmetry Methods for Differential Equations written by Peter Ellsworth Hydon and published by Cambridge University Press. This book was released on 2000-01-28 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a straightforward introduction to the subject of symmetry methods for solving differential equations, and is aimed at applied mathematicians, physicists, and engineers. The presentation is informal, using many worked examples to illustrate the main symmetry methods. It is written at a level suitable for postgraduates and advanced undergraduates, and is designed to enable the reader to master the main techniques quickly and easily.The book contains some methods that have not previously appeared in a text. These include methods for obtaining discrete symmetries and integrating factors.
Book Synopsis Partial Differential Equations by : Walter A. Strauss
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Book Synopsis Symmetry and Separation of Variables for the Hamilton-Jacobi Equation by : Charles P. Boyer
Download or read book Symmetry and Separation of Variables for the Hamilton-Jacobi Equation written by Charles P. Boyer and published by . This book was released on 1976 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Symmetry and Separation of Variables for the Hamilton-Jacobi Equation Wt2-Wx2-Wy2 by : Charles P. Boyer
Download or read book Symmetry and Separation of Variables for the Hamilton-Jacobi Equation Wt2-Wx2-Wy2 written by Charles P. Boyer and published by . This book was released on 1976 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Symmetry and separation of variables for the Hamilton-Jacobi equation ... by : Charles P. Boyer
Download or read book Symmetry and separation of variables for the Hamilton-Jacobi equation ... written by Charles P. Boyer and published by . This book was released on 1976 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Separation of Variables for Riemannian Spaces of Constant Curvature by : E. G. Kalnins
Download or read book Separation of Variables for Riemannian Spaces of Constant Curvature written by E. G. Kalnins and published by Longman Scientific and Technical. This book was released on 1986 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive and up-to-date survey of research on torsion theories defined on module categories over noncommutative rings and the use in the localization of rings and modules.
Book Synopsis Symmetry and Separation of Variables for the Hamilton-jacobi Equation W@ - W@ - W@ by : C. P. Boyer
Download or read book Symmetry and Separation of Variables for the Hamilton-jacobi Equation W@ - W@ - W@ written by C. P. Boyer and published by . This book was released on 1976 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Partial Differential Equations and Boundary-Value Problems with Applications by : Mark A. Pinsky
Download or read book Partial Differential Equations and Boundary-Value Problems with Applications written by Mark A. Pinsky and published by American Mathematical Soc.. This book was released on 2011 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.
Book Synopsis An Algebraic Geometric Approach to Separation of Variables by : Konrad Schöbel
Download or read book An Algebraic Geometric Approach to Separation of Variables written by Konrad Schöbel and published by Springer. This book was released on 2015-10-15 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: Konrad Schöbel aims to lay the foundations for a consequent algebraic geometric treatment of variable Separation, which is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum physics. The present work reveals a surprising algebraic geometric structure behind the famous list of separation coordinates, bringing together a great range of mathematics and mathematical physics, from the late 19th century theory of separation of variables to modern moduli space theory, Stasheff polytopes and operads. "I am particularly impressed by his mastery of a variety of techniques and his ability to show clearly how they interact to produce his results.” (Jim Stasheff)
Book Synopsis Contributions to the Study of the Separation of Variables and Symmetry Operators for Relativistic Wave Equations on Curved Spacetime by : Niky Kamran
Download or read book Contributions to the Study of the Separation of Variables and Symmetry Operators for Relativistic Wave Equations on Curved Spacetime written by Niky Kamran and published by . This book was released on 1984 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt:
