Algebraic Approach To Differential Equations

Author : D?ng Tr ng Lˆ
Publisher : World Scientific
Page : 320 pages
File Size : 53,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814273244

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Algebraic Approach to Differential Equations by D?ng Tr ng Lˆ Pdf

Mixing elementary results and advanced methods, Algebraic Approach to Differential Equations aims to accustom differential equation specialists to algebraic methods in this area of interest. It presents material from a school organized by The Abdus Salam International Centre for Theoretical Physics (ICTP), the Bibliotheca Alexandrina, and the International Centre for Pure and Applied Mathematics (CIMPA).

Author : M. Matsuda
Publisher : Springer
Page : 118 pages
File Size : 53,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540393115

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First Order Algebraic Differential Equations by M. Matsuda Pdf

Author : Anindya Dey
Publisher : CRC Press
Page : 522 pages
File Size : 45,8 Mb
Release : 2021-09-27
Category : Mathematics
ISBN : 9781000436792

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Differential Equations by Anindya Dey Pdf

Differential Equations: A Linear Algebra Approach follows an innovative approach of inculcating linear algebra and elementary functional analysis in the backdrop of even the simple methods of solving ordinary differential equations. The contents of the book have been made user-friendly through concise useful theoretical discussions and numerous illustrative examples practical and pathological.

Author : Xiaoping Xu
Publisher : Springer
Page : 0 pages
File Size : 46,9 Mb
Release : 2015-05-19
Category : Mathematics
ISBN : 3642427626

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Algebraic Approaches to Partial Differential Equations by Xiaoping Xu Pdf

This book presents the various algebraic techniques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations such as: the Maxwell equations, the Dirac equations, the KdV equation, the KP equation, the nonlinear Schrodinger equation, the Davey and Stewartson equations, the Boussinesq equations in geophysics, the Navier-Stokes equations and the boundary layer problems. In order to solve them, I have employed the grading technique, matrix differential operators, stable-range of nonlinear terms, moving frames, asymmetric assumptions, symmetry transformations, linearization techniques and special functions. The book is self-contained and requires only a minimal understanding of calculus and linear algebra, making it accessible to a broad audience in the fields of mathematics, the sciences and engineering. Readers may find the exact solutions and mathematical skills needed in their own research.

Author : International Centre for Theoretical Physics
Publisher : Unknown
Page : 312 pages
File Size : 42,9 Mb
Release : 2010
Category : Differential equations
ISBN : 9784273233

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Algebraic Approach to Differential Equations by International Centre for Theoretical Physics Pdf

Author : Joseph Fels Ritt
Publisher : American Mathematical Soc.
Page : 184 pages
File Size : 52,9 Mb
Release : 1932-12-31
Category : Mathematics
ISBN : 9780821846056

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Differential Equations from the Algebraic Standpoint by Joseph Fels Ritt Pdf

This book can be viewed as a first attempt to systematically develop an algebraic theory of nonlinear differential equations, both ordinary and partial. The main goal of the author was to construct a theory of elimination, which ``will reduce the existence problem for a finite or infinite system of algebraic differential equations to the application of the implicit function theorem taken with Cauchy's theorem in the ordinary case and Riquier's in the partial.'' In his 1934 review of the book, J. M. Thomas called it ``concise, readable, original, precise, and stimulating'', and his words still remain true. A more fundamental and complete account of further developments of the algebraic approach to differential equations is given in Ritt's treatise Differential Algebra, written almost 20 years after the present work (Colloquium Publications, Vol. 33, American Mathematical Society, 1950).

Author : Bernd Simeon
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 54,5 Mb
Release : 2013-06-14
Category : Mathematics
ISBN : 9783642351587

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Computational Flexible Multibody Dynamics by Bernd Simeon Pdf

This monograph, written from a numerical analysis perspective, aims to provide a comprehensive treatment of both the mathematical framework and the numerical methods for flexible multibody dynamics. Not only is this field permanently and rapidly growing, with various applications in aerospace engineering, biomechanics, robotics, and vehicle analysis, its foundations can also be built on reasonably established mathematical models. Regarding actual computations, great strides have been made over the last two decades, as sophisticated software packages are now capable of simulating highly complex structures with rigid and deformable components. The approach used in this book should benefit graduate students and scientists working in computational mechanics and related disciplines as well as those interested in time-dependent partial differential equations and heterogeneous problems with multiple time scales. Additionally, a number of open issues at the frontiers of research are addressed by taking a differential-algebraic approach and extending it to the notion of transient saddle point problems.

Author : Michihiko Matsuda,Oldřich Kowalski
Publisher : Unknown
Page : 109 pages
File Size : 46,5 Mb
Release : 1980
Category : Burnside problem
ISBN : 0387099972

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Burnside Groups by Michihiko Matsuda,Oldřich Kowalski Pdf

Author : P.H. Kersten,I.S. Krasil'shchik
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400901797

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Geometric and Algebraic Structures in Differential Equations by P.H. Kersten,I.S. Krasil'shchik Pdf

The geometrical theory of nonlinear differential equations originates from classical works by S. Lie and A. Bäcklund. It obtained a new impulse in the sixties when the complete integrability of the Korteweg-de Vries equation was found and it became clear that some basic and quite general geometrical and algebraic structures govern this property of integrability. Nowadays the geometrical and algebraic approach to partial differential equations constitutes a special branch of modern mathematics. In 1993, a workshop on algebra and geometry of differential equations took place at the University of Twente (The Netherlands), where the state-of-the-art of the main problems was fixed. This book contains a collection of invited lectures presented at this workshop. The material presented is of interest to those who work in pure and applied mathematics and especially in mathematical physics.

Author : René Lamour,Roswitha März,Caren Tischendorf
Publisher : Springer Science & Business Media
Page : 667 pages
File Size : 47,8 Mb
Release : 2013-01-19
Category : Mathematics
ISBN : 9783642275555

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Differential-Algebraic Equations: A Projector Based Analysis by René Lamour,Roswitha März,Caren Tischendorf Pdf

Differential algebraic equations (DAEs), including so-called descriptor systems, began to attract significant research interest in applied and numerical mathematics in the early 1980s, no more than about three decades ago. In this relatively short time, DAEs have become a widely acknowledged tool to model processes subjected to constraints, in order to simulate and to control processes in various application fields such as network simulation, chemical kinematics, mechanical engineering, system biology. DAEs and their more abstract versions in infinite-dimensional spaces comprise a great potential for future mathematical modeling of complex coupled processes. The purpose of the book is to expose the impressive complexity of general DAEs from an analytical point of view, to describe the state of the art as well as open problems and so to motivate further research to this versatile, extra-ordinary topic from a broader mathematical perspective. The book elaborates a new general structural analysis capturing linear and nonlinear DAEs in a hierarchical way. The DAE structure is exposed by means of special projector functions. Numerical integration issues and computational aspects are treated also in this context.

Author : Danuta Przeworska-Rolewicz
Publisher : Elsevier Science & Technology
Page : 380 pages
File Size : 49,7 Mb
Release : 1973
Category : Mathematics
ISBN : UOM:39015077980236

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Equations with Transformed Argument by Danuta Przeworska-Rolewicz Pdf

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 46,7 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9789814467964

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Algebraic Approach to Differential Equations by Anonim Pdf

Author : Todd Kapitula
Publisher : SIAM
Page : 308 pages
File Size : 44,6 Mb
Release : 2015-11-17
Category : Mathematics
ISBN : 9781611974096

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Ordinary Differential Equations and Linear Algebra by Todd Kapitula Pdf

Ordinary differential equations (ODEs) and linear algebra are foundational postcalculus mathematics courses in the sciences. The goal of this text is to help students master both subject areas in a one-semester course. Linear algebra is developed first, with an eye toward solving linear systems of ODEs. A computer algebra system is used for intermediate calculations (Gaussian elimination, complicated integrals, etc.); however, the text is not tailored toward a particular system.?Ordinary Differential Equations and Linear Algebra: A Systems Approach?systematically develops the linear algebra needed to solve systems of ODEs and includes over 15 distinct applications of the theory, many of which are not typically seen in a textbook at this level (e.g., lead poisoning, SIR models, digital filters). It emphasizes mathematical modeling and contains group projects at the end of each chapter that allow students to more fully explore the interaction between the modeling of a system, the solution of the model, and the resulting physical description.?

Author : Uri M. Ascher,Linda R. Petzold
Publisher : SIAM
Page : 305 pages
File Size : 55,9 Mb
Release : 1998-01-01
Category : Mathematics
ISBN : 161197139X

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Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations by Uri M. Ascher,Linda R. Petzold Pdf

Designed for those people who want to gain a practical knowledge of modern techniques, this book contains all the material necessary for a course on the numerical solution of differential equations. Written by two of the field's leading authorities, it provides a unified presentation of initial value and boundary value problems in ODEs as well as differential-algebraic equations. The approach is aimed at a thorough understanding of the issues and methods for practical computation while avoiding an extensive theorem-proof type of exposition. It also addresses reasons why existing software succeeds or fails. This book is a practical and mathematically well-informed introduction that emphasizes basic methods and theory, issues in the use and development of mathematical software, and examples from scientific engineering applications. Topics requiring an extensive amount of mathematical development, such as symplectic methods for Hamiltonian systems, are introduced, motivated, and included in the exercises, but a complete and rigorous mathematical presentation is referenced rather than included.

Author : Barry G. Adams
Publisher : Springer Science & Business Media
Page : 457 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642579332

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Algebraic Approach to Simple Quantum Systems by Barry G. Adams Pdf

This book provides an introduction to the use of algebraic methods and sym bolic computation for simple quantum systems with applications to large order perturbation theory. It is the first book to integrate Lie algebras, algebraic perturbation theory and symbolic computation in a form suitable for students and researchers in theoretical and computational chemistry and is conveniently divided into two parts. The first part, Chapters 1 to 6, provides a pedagogical introduction to the important Lie algebras so(3), so(2,1), so(4) and so(4,2) needed for the study of simple quantum systems such as the D-dimensional hydrogen atom and harmonic oscillator. This material is suitable for advanced undergraduate and beginning graduate students. Of particular importance is the use of so(2,1) in Chapter 4 as a spectrum generating algebra for several important systems such as the non-relativistic hydrogen atom and the relativistic Klein-Gordon and Dirac equations. This approach provides an interesting and important alternative to the usual textbook approach using series solutions of differential equations.