# symmetric differential equations

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## Symmetry Analysis Of Differential Equations

**Author :**Daniel J. Arrigo

**ISBN :**9781118721407

**Genre :**Mathematics

**File Size :**24. 51 MB

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A SELF-CONTAINED INTRODUCTION TO THE METHODS AND TECHNIQUESOF SYMMETRY ANALYSIS USED TO SOLVE ODEs AND PDEs Symmetry Analysis of Differential Equations: AnIntroduction presents an accessible approach to the uses ofsymmetry methods in solving both ordinary differential equations(ODEs) and partial differential equations (PDEs). Providingcomprehensive coverage, the book fills a gap in the literature bydiscussing elementary symmetry concepts and invariance, includingmethods for reducing the complexity of ODEs and PDEs in an effortto solve the associated problems. Thoroughly class-tested, the author presents classical methods in asystematic, logical, and well-balanced manner. As the bookprogresses, the chapters graduate from elementary symmetries andthe invariance of algebraic equations, to ODEs and PDEs, followedby coverage of the nonclassical method and compatibility.Symmetry Analysis of Differential Equations: An Introductionalso features: Detailed, step-by-step examples to guide readers through themethods of symmetry analysis End-of-chapter exercises, varying from elementary to advanced,with select solutions to aid in the calculation of the presentedalgorithmic methods Symmetry Analysis of Differential Equations: An Introduction isan ideal textbook for upper-undergraduate and graduate-levelcourses in symmetry methods and applied mathematics. The book isalso a useful reference for professionals in science, physics, andengineering, as well as anyone wishing to learn about the use ofsymmetry methods in solving differential equations. DANIEL J. ARRIGO, PhD, is Professor in the Department ofMathematics at the University of Central Arkansas. The author ofover 30 journal articles, his research interests include theconstruction of exact solutions of PDEs; symmetry analysis ofnonlinear PDEs; and solutions to physically important equations,such as nonlinear heat equations and governing equations modelingof granular materials and nonlinear elasticity. In 2008, Dr. Arrigoreceived the Oklahoma-Arkansas Section of the MathematicalAssociation of America’s Award for Distinguished Teaching ofCollege or University Mathematics.

## Symmetry Methods For Differential Equations

**Author :**Peter E. Hydon

**ISBN :**0521497868

**Genre :**Mathematics

**File Size :**64. 20 MB

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An introduction to symmetry methods, informally written and aimed at applied mathematicians, physicists, and engineers.

## Symmetry Analysis Of Differential Equations With Mathematica

**Author :**Gerd Baumann

**ISBN :**9781461221104

**Genre :**Mathematics

**File Size :**53. 14 MB

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The first book to explicitly use Mathematica so as to allow researchers and students to more easily compute and solve almost any kind of differential equation using Lie's theory. Previously time-consuming and cumbersome calculations are now much more easily and quickly performed using the Mathematica computer algebra software. The material in this book, and on the accompanying CD-ROM, will be of interest to a broad group of scientists, mathematicians and engineers involved in dealing with symmetry analysis of differential equations. Each section of the book starts with a theoretical discussion of the material, then shows the application in connection with Mathematica. The cross-platform CD-ROM contains Mathematica (version 3.0) notebooks which allow users to directly interact with the code presented within the book. In addition, the author's proprietary "MathLie" software is included, so users can readily learn to use this powerful tool in regard to performing algebraic computations.

## Symmetry And Integration Methods For Differential Equations

**Author :**George Bluman

**ISBN :**9780387216492

**Genre :**Mathematics

**File Size :**88. 43 MB

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This text discusses Lie groups of transformations and basic symmetry methods for solving ordinary and partial differential equations. It places emphasis on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This new edition covers contact transformations, Lie-B cklund transformations, and adjoints and integrating factors for ODEs of arbitrary order.

## Applications Of Symmetry Methods To Partial Differential Equations

**Author :**George W. Bluman

**ISBN :**9780387680286

**Genre :**Mathematics

**File Size :**52. 52 MB

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This is an acessible book on the advanced symmetry methods for differential equations, including such subjects as conservation laws, Lie-Bäcklund symmetries, contact transformations, adjoint symmetries, Nöther's Theorem, mappings with some modification, potential symmetries, nonlocal symmetries, nonlocal mappings, and non-classical method. Of use to graduate students and researchers in mathematics and physics.

## Applications Of Lie Groups To Differential Equations

**Author :**Peter J. Olver

**ISBN :**9781468402742

**Genre :**Mathematics

**File Size :**28. 29 MB

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This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.

## Ordinary And Partial Differential Equations

**Author :**P Smith

**ISBN :**0582305896

**Genre :**Mathematics

**File Size :**54. 73 MB

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These conference proceedings include papers by a number of experts with a common interest in differential equations and their application in physical and biological systems. Topics covered include direct and inverse electromagnetic scattering techniques, spatial epidemic models, wound healing, chemotaxis and reaction-diffusion equations, dynamics and stability of thin liquid films, and a contemporary formulation of symmetric linear differential equations.

## Handbook Of Differential Equations Stationary Partial Differential Equations

**Author :**Michel Chipot

**ISBN :**0080557317

**Genre :**Mathematics

**File Size :**24. 19 MB

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A collection of self contained state-of-the art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching. * Written by well-known experts in the field * Self contained volume in series covering one of the most rapid developing topics in mathematics * Informed and thoroughly updated for students, academics and researchers

## Algorithmic Lie Theory For Solving Ordinary Differential Equations

**Author :**Fritz Schwarz

**ISBN :**1584888903

**Genre :**Mathematics

**File Size :**57. 75 MB

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Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete problems. Taking this approach, Algorithmic Lie Theory for Solving Ordinary Differential Equations serves as a valuable introduction for solving differential equations using Lie's theory and related results. After an introductory chapter, the book provides the mathematical foundation of linear differential equations, covering Loewy's theory and Janet bases. The following chapters present results from the theory of continuous groups of a 2-D manifold and discuss the close relation between Lie's symmetry analysis and the equivalence problem. The core chapters of the book identify the symmetry classes to which quasilinear equations of order two or three belong and transform these equations to canonical form. The final chapters solve the canonical equations and produce the general solutions whenever possible as well as provide concluding remarks. The appendices contain solutions to selected exercises, useful formulae, properties of ideals of monomials, Loewy decompositions, symmetries for equations from Kamke's collection, and a brief description of the software system ALLTYPES for solving concrete algebraic problems.

## Nonlinear Partial Differential Equations In Engineering And Applied Science

**Author :**Robert L. Sternberg

**ISBN :**0824769961

**Genre :**Mathematics

**File Size :**60. 69 MB

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In this volume are twenty-eight papers from the Conference on Nonlinear Partial Differential Equationsin Engineering and Applied Science, sponsored by the Office of Naval Research and held at the Universityof Rhode Island in June, 1979. Included are contributions from an international group of distinguishedmathematicians, scientists, and engineers coming from a wide variety of disciplines and having a commoninterest in the application of mathematics, particularly nonlinear partial differential equations, to realworld problems.The subject matter ranges from almost purely mathematical topics in numerical analysis and bifurcationtheory to a host of practical applications that involve nonlinear partial differential equations, suchas fluid dynamics, nonlinear waves, elasticity, viscoelasticity, hyperelasticity, solitons, metallurgy, shocklessairfoil design, quantum fields, and Darcy's law on flows in porous media.Non/inear Partial Differential Equations in Engineering and Applied Science focuses on a variety oftopics of specialized, contemporary concern to mathematicians, physical and biological scientists, andengineers who work with phenomena that can be described by nonlinear partial differential equations.