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Lectures on the Theory of Group Properties of Differential Equations

Lectures on the Theory of Group Properties of Differential Equations Author L V Ovsyannikov
ISBN-10 9789814460835
Release 2013-05-20
Pages 156
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These lecturers provide a clear introduction to Lie group methods for determining and using symmetries of differential equations, a variety of their applications in gas dynamics and other nonlinear models as well as the author's remarkable contribution to this classical subject. It contains material that is useful for students and teachers but cannot be found in modern texts. For example, the theory of partially invariant solutions developed by Ovsyannikov provides a powerful tool for solving systems of nonlinear differential equations and investigating complicated mathematical models.



Applications of Lie Groups to Differential Equations

Applications of Lie Groups to Differential Equations Author Peter J. Olver
ISBN-10 0387950001
Release 2000-01-21
Pages 513
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This is a solid introduction to applications of Lie groups to differential equations which have proved to be useful in practice. Following an exposition of the applications, the book develops the underlying theory, with many of the topics presented in a novel way, emphasizing explicit examples and computations. Further examples and new theoretical developments appear in the exercises at the end of each chapter.



Group Properties Of The Acoustic Differential Equation

Group Properties Of The Acoustic Differential Equation Author L V Poluyanov
ISBN-10 9781482272659
Release 2014-04-21
Pages 166
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This text is an addition to the existing literature about the symmetrical properties of sound waves. The authors clarify the algebraic and analytical nature of the dynamic acoustic problem. Operator equations which are typical for linear systems and the more general Lie method are considered, which can be applied even to nonlinear problems. The information obtained allows the reader to construct different types of analytical solutions of the different acoustic equation. The acoustic differential equation describes sound waves in elastic media. If the media is non-homogeneous then the acoustic equation is generally very complicated and its exact solutions or analytical solutions may be considered as rare. This volume applies Lie algebra and Lie group techniques to separate independent variables and obtains exact analytical solutions. Special attention is paid to homogeneous and non-homogeneous media with different symmetry properties. The full wave acoustic equation is considered as well as the so-called phase acoustic equation which arises in the short-wave approximation.



Lectures on Ordinary Differential Equations

Lectures on Ordinary Differential Equations Author Witold Hurewicz
ISBN-10 9780486797212
Release 2014-07-21
Pages 144
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Introductory treatment explores existence theorems for first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. "A rigorous and lively introduction." — The American Mathematical Monthly. 1958 edition.



Lectures on Analytic Differential Equations

Lectures on Analytic Differential Equations Author I͡U. S. Ilʹi͡ashenko
ISBN-10 0821872486
Release
Pages 625
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Each section ends with a collection of problems, partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the more recent results surveyed in the text." "The exposition of the book is mostly geometric, though the algebraic side of the constructions is also prominently featured. On several occasions the reader is introduced to adjacent areas, such as intersection theory for divisors on the projective plane or geometric theory of holomorphic vector bundles with meromorphic connections. The book provides the reader with the principal tools of the modern theory of analytic differential equations and intends to serve as a standard source for references in this area."--BOOK JACKET.



Geometrical Properties of Differential Equations

Geometrical Properties of Differential Equations Author Ljudmila A Bordag
ISBN-10 9789814667265
Release 2015-05-27
Pages 340
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This textbook is a short comprehensive and intuitive introduction to Lie group analysis of ordinary and partial differential equations. This practical-oriented material contains a large number of examples and problems accompanied by detailed solutions and figures. In comparison with the known beginner guides to Lie group analysis, the book is oriented toward students who are interested in financial mathematics, mathematical finance and economics. We provide the results of the Lie group analysis of actual models in Financial Mathematics using recent publications. These models are usually formulated as nonlinear partial differential equations and are rather difficult to make use of. With the help of Lie group analysis it is possible to describe some important properties of these models and to obtain interesting reductions in a clear and understandable algorithmic way. The book can serve as a short introduction for a further study of modern geometrical analysis applied to models in financial mathematics. It can also be used as textbook in a master's program, in an intensive compact course, or for self study. The textbook with a large number of examples will be useful not only for students who are interested in Financial Mathematics but also for people who are working in other areas of research that are not directly connected with Physics (for instance in such areas of Applied Mathematics like mathematical economy, bio systems, coding theory, etc.).



Equadiff 7 Partial differential equations Numerical methods applications

Equadiff 7    Partial differential equations  Numerical methods   applications Author
ISBN-10 UOM:39015019565848
Release 1989
Pages
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Equadiff 7 Partial differential equations Numerical methods applications has been writing in one form or another for most of life. You can find so many inspiration from Equadiff 7 Partial differential equations Numerical methods applications also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Equadiff 7 Partial differential equations Numerical methods applications book for free.



Linear Differential Equations and Group Theory from Riemann to Poincare

Linear Differential Equations and Group Theory from Riemann to Poincare Author Jeremy Gray
ISBN-10 0817647724
Release 2008-01-21
Pages 338
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This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry. The text for this second edition has been greatly expanded and revised, and the existing appendices enriched. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.



Lectures on Analytic Differential Equations

Lectures on Analytic Differential Equations Author I͡U. S. Ilʹi͡ashenko
ISBN-10 9780821836675
Release 2008
Pages 625
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The book combines the features of a graduate-level textbook with those of a research monograph and survey of the recent results on analysis and geometry of differential equations in the real and complex domain. As a graduate textbook, it includes self-contained, sometimes considerably simplified demonstrations of several fundamental results, which previously appeared only in journal publications (desingularization of planar analytic vector fields, existence of analytic separatrices, positive and negative results on the Riemann-Hilbert problem, Ecalle-Voronin and Martinet-Ramis moduli, solution of the Poincare problem on the degree of an algebraic separatrix, etc.). As a research monograph, it explores in a systematic way the algebraic decidability of local classification problems, rigidity of holomorphic foliations, etc. Each section ends with a collection of problems, partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the more recent results surveyed in the text. The exposition of the book is mostly geometric, though the algebraic side of the constructions is also prominently featured. On several occasions the reader is introduced to adjacent areas, such as intersection theory for divisors on the projective plane or geometric theory of holomorphic vector bundles with meromorphic connections. The book provides the reader with the principal tools of the modern theory of analytic differential equations and intends to serve as a standard source for references in this area.



Lectures on mixed problems in partial differential equations and representation of semi groups

Lectures on mixed problems in partial differential equations and representation of semi groups Author Laurent Schwartz
ISBN-10 UOM:39015017420509
Release 1957
Pages 236
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Lectures on mixed problems in partial differential equations and representation of semi groups has been writing in one form or another for most of life. You can find so many inspiration from Lectures on mixed problems in partial differential equations and representation of semi groups also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Lectures on mixed problems in partial differential equations and representation of semi groups book for free.



Group Theory and Numerical Analysis

Group Theory and Numerical Analysis Author Pavel Winternitz
ISBN-10 0821870343
Release
Pages 298
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The Workshop on Group Theory and Numerical Analysis brought together scientists working in several different but related areas. The unifying theme was the application of group theory and geometrical methods to the solution of differential and difference equations. The emphasis was on the combination of analytical and numerical methods and also the use of symbolic computation. This meeting was organized under the auspices of the Centre de Recherches Mathematiques, Universite de Montreal (Canada). This volume has the character of a monograph and should represent a useful reference book for scientists working in this highly topical field.



Hyperbolic Partial Differential Equations

Hyperbolic Partial Differential Equations Author Matthew Witten
ISBN-10 9781483151359
Release 2014-05-23
Pages 268
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Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic McKendrick equations for age-structured population growth; and logistic models of structured population growth. A number of book reviews are also included. This journal provides an interdisciplinary forum for the presentation of results not included in other particular journals, and thus will be beneficial to those interested in this field of study.



Lectures on Algebraic Topology

Lectures on Algebraic Topology Author Sergeĭ Vladimirovich Matveev
ISBN-10 303719023X
Release 2006
Pages 99
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Algebraic topology is the study of the global properties of spaces by means of algebra. It is an important branch of modern mathematics with a wide degree of applicability to other fields, including geometric topology, differential geometry, functional analysis, differential equations, algebraic geometry, number theory, and theoretical physics. This book provides an introduction to the basic concepts and methods of algebraic topology for the beginner. It presents elements of both homology theory and homotopy theory, and includes various applications. The author's intention is to rely on the geometric approach by appealing to the reader's own intuition to help understanding. The numerous illustrations in the text also serve this purpose. Two features make the text different from the standard literature: first, special attention is given to providing explicit algorithms for calculating the homology groups and for manipulating the fundamental groups. Second, the book contains many exercises, all of which are supplied with hints or solutions. This makes the book suitable for both classroom use and for independent study.



Trends in Theory and Practice of Nonlinear Differential Equations

Trends in Theory and Practice of Nonlinear Differential Equations Author V. Lakshmikantham
ISBN-10 0824771303
Release 1984-01-03
Pages 592
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Trends in Theory and Practice of Nonlinear Differential Equations has been writing in one form or another for most of life. You can find so many inspiration from Trends in Theory and Practice of Nonlinear Differential Equations also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Trends in Theory and Practice of Nonlinear Differential Equations book for free.



Differential Equations

Differential Equations Author K.D. Elworthy
ISBN-10 9781351455206
Release 2017-11-22
Pages 984
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Presents recent developments in the areas of differential equations, dynamical systems, and control of finke and infinite dimensional systems. Focuses on current trends in differential equations and dynamical system research-from Darameterdependence of solutions to robui control laws for inflnite dimensional systems.



Proceedings of the Conference on Differential Equations and the Stokes Phenomenon

Proceedings of the Conference on Differential Equations and the Stokes Phenomenon Author Boele Lieuwe Jan Braaksma
ISBN-10 9812381724
Release 2002
Pages 329
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Offers a snapshot concerning the state of the art in the areas of differential, difference and q-difference equations.



Generalized Solutions of Functional Differential Equations

Generalized Solutions of Functional Differential Equations Author Joseph Wiener
ISBN-10 9810212070
Release 1993
Pages 410
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The need to investigate functional differential equations with discontinuous delays is addressed in this book. Recording the work and findings of several scientists on differential equations with piecewise continuous arguments over the last few years, this book serves as a useful source of reference. Great interest is placed on discussing the stability, oscillation and periodic properties of the solutions. Considerable attention is also given to the study of initial and boundary-value problems for partial differential equations of mathematical physics with discontinuous time delays. In fact, a large part of the book is devoted to the exploration of differential and functional differential equations in spaces of generalized functions (distributions) and contains a wealth of new information in this area. Each topic discussed appears to provide ample opportunity for extending the known results. A list of new research topics and open problems is also included as an update.