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Lectures On The Theory Of Group Properties Of Differential Equations

Author: L V Ovsyannikov
Publisher: World Scientific Publishing Company
ISBN: 9814460834
Size: 46.47 MB
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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.

Group Properties Of The Acoustic Differential Equation

Author: L V Poluyanov
Publisher: CRC Press
ISBN: 9780748402809
Size: 35.53 MB
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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 Analytic Differential Equations

Author: I͡U. S. Ilʹi͡ashenko
Publisher: American Mathematical Soc.
ISBN: 9780821872482
Size: 54.18 MB
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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.

Linear Differential Equations And Group Theory From Riemann To Poincare

Author: Jeremy Gray
Publisher: Springer Science & Business Media
ISBN: 9780817647728
Size: 54.17 MB
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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.

Applications Of Lie Groups To Differential Equations

Author: Peter J. Olver
Publisher: Springer Science & Business Media
ISBN: 9780387950006
Size: 38.59 MB
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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.

Hyperbolic Partial Differential Equations

Author: Matthew Witten
Publisher: Elsevier
ISBN: 1483151352
Size: 19.14 MB
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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.

Emergence Of The Theory Of Lie Groups

Author: Thomas Hawkins
Publisher: Springer Science & Business Media
ISBN: 9780387989631
Size: 74.26 MB
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The great Norwegian mathematician Sophus Lie developed the general theory of transformations in the 1870s, and the first part of the book properly focuses on his work. In the second part the central figure is Wilhelm Killing, who developed structure and classification of semisimple Lie algebras. The third part focuses on the developments of the representation of Lie algebras, in particular the work of Elie Cartan. The book concludes with the work of Hermann Weyl and his contemporaries on the structure and representation of Lie groups which serves to bring together much of the earlier work into a coherent theory while at the same time opening up significant avenues for further work.

Differential Equations

Author: K.D. Elworthy
Publisher: CRC Press
ISBN: 9780824789046
Size: 73.99 MB
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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.