Symmetry And Separation Of Variables PDF Download
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Author | : Willard Miller |
Publisher | : Cambridge University Press |
Total Pages | : 0 |
Release | : 2012-03-29 |
Genre | : Mathematics |
ISBN | : 9780521177399 |
Download Symmetry and Separation of Variables Book in PDF, ePub and Kindle
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.
Author | : Willard Miller |
Publisher | : |
Total Pages | : 320 |
Release | : 2014-05-14 |
Genre | : SCIENCE |
ISBN | : 9781107087460 |
Download Symmetry and Separation of Variables Book in PDF, ePub and Kindle
This 1977 volume is concerned with the group-theoretic approach to special functions.
Author | : E. G. Kalnins |
Publisher | : IOP Publishing Limited |
Total Pages | : 0 |
Release | : 2018 |
Genre | : Science |
ISBN | : 9780750313155 |
Download Separation of Variables and Superintegrability Book in PDF, ePub and Kindle
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.
Author | : Andrei D. Polyanin |
Publisher | : CRC Press |
Total Pages | : 349 |
Release | : 2021-09-20 |
Genre | : Mathematics |
ISBN | : 1000463664 |
Download Separation of Variables and Exact Solutions to Nonlinear PDEs Book in PDF, ePub and Kindle
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.
Author | : Willard Miller, Jr |
Publisher | : |
Total Pages | : 326 |
Release | : 2018-06-13 |
Genre | : |
ISBN | : 9780750317863 |
Download Separation of Variables and Superintegrability Book in PDF, ePub and Kindle
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.
Author | : Walter A. Strauss |
Publisher | : John Wiley & Sons |
Total Pages | : 467 |
Release | : 2007-12-21 |
Genre | : Mathematics |
ISBN | : 0470054565 |
Download Partial Differential Equations Book in PDF, ePub and Kindle
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.
Author | : Peter Ellsworth Hydon |
Publisher | : Cambridge University Press |
Total Pages | : 230 |
Release | : 2000-01-28 |
Genre | : Mathematics |
ISBN | : 9780521497862 |
Download Symmetry Methods for Differential Equations Book in PDF, ePub and Kindle
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.
Author | : George W. Bluman |
Publisher | : Springer Science & Business Media |
Total Pages | : 424 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 1475743076 |
Download Symmetries and Differential Equations Book in PDF, ePub and Kindle
A major portion of this book discusses work which has appeared since the publication of the book Similarity Methods for Differential Equations, Springer-Verlag, 1974, by the first author and J.D. Cole. The present book also includes a thorough and comprehensive treatment of Lie groups of tranformations and their various uses for solving ordinary and partial differential equations. No knowledge of group theory is assumed. Emphasis is placed on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This book should be particularly suitable for physicists, applied mathematicians, and engineers. Almost all of the examples are taken from physical and engineering problems including those concerned with heat conduction, wave propagation, and fluid flows. A preliminary version was used as lecture notes for a two-semester course taught by the first author at the University of British Columbia in 1987-88 to graduate and senior undergraduate students in applied mathematics and physics. Chapters 1 to 4 encompass basic material. More specialized topics are covered in Chapters 5 to 7.
Author | : Mark A. Pinsky |
Publisher | : American Mathematical Soc. |
Total Pages | : 545 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 0821868896 |
Download Partial Differential Equations and Boundary-Value Problems with Applications Book in PDF, ePub and Kindle
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.
Author | : Brian Cantwell |
Publisher | : Cambridge University Press |
Total Pages | : 660 |
Release | : 2002-09-23 |
Genre | : Mathematics |
ISBN | : 9780521777407 |
Download Introduction to Symmetry Analysis Paperback with CD-ROM Book in PDF, ePub and Kindle
An introduction to symmetry analysis for graduate students in science, engineering and applied mathematics.