Lectures On The Theory Of Group Properties Of Differential Equations

Author : L V Ovsyannikov
Publisher : World Scientific Publishing Company
ISBN 13 : 9814460834
Total Pages : 156 pages
Book Rating : 4.35/5 ( download)

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Download or read book Lectures on the Theory of Group Properties of Differential Equations written by L V Ovsyannikov and published by World Scientific Publishing Company. This book was released on 2013-05-20 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : L. V. Ovsyannikov
Publisher :
ISBN 13 : 9787894236319
Total Pages : 141 pages
Book Rating : 4.14/5 ( download)

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Download or read book Lectures on the Theory of Group Properties of Differential Equations written by L. V. Ovsyannikov and published by . This book was released on with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : L V Poluyanov
Publisher : CRC Press
ISBN 13 : 9780748402809
Total Pages : 170 pages
Book Rating : 4.02/5 ( download)

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Download or read book Group Properties Of The Acoustic Differential Equation written by L V Poluyanov and published by CRC Press. This book was released on 1995-05-24 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Lawrence Markus
Publisher :
ISBN 13 :
Total Pages : 246 pages
Book Rating : 4.93/5 ( download)

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Download or read book Group Theory and Differential Equations written by Lawrence Markus and published by . This book was released on 1960 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Andy R. Magid
Publisher : American Mathematical Soc.
ISBN 13 : 0821870041
Total Pages : 119 pages
Book Rating : 4.44/5 ( download)

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Download or read book Lectures on Differential Galois Theory written by Andy R. Magid and published by American Mathematical Soc.. This book was released on 1994 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Galois theory studies solutions of differential equations over a differential base field. In much the same way that ordinary Galois theory is the theory of field extensions generated by solutions of (one variable) polynomial equations, differential Galois theory looks at the nature of the differential field extension generated by the solution of differential equations. An additional feature is that the corresponding differential Galois groups (of automorphisms of the extension fixing the base and commuting with the derivation) are algebraic groups. This book deals with the differential Galois theory of linear homogeneous differential equations, whose differential Galois groups are algebraic matrix groups. In addition to providing a convenient path to Galois theory, this approach also leads to the constructive solution of the inverse problem of differential Galois theory for various classes of algebraic groups. Providing a self-contained development and many explicit examples, this book provides a unique approach to differential Galois theory and is suitable as a textbook at the advanced graduate level.

Author : Alexander Nagel
Publisher : Princeton University Press
ISBN 13 : 1400870488
Total Pages : 167 pages
Book Rating : 4.86/5 ( download)

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Download or read book Lectures on Pseudo-Differential Operators written by Alexander Nagel and published by Princeton University Press. This book was released on 2015-03-08 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of pseudo-differential operators (which originated as singular integral operators) was largely influenced by its application to function theory in one complex variable and regularity properties of solutions of elliptic partial differential equations. Given here is an exposition of some new classes of pseudo-differential operators relevant to several complex variables and certain non-elliptic problems. Originally published in 1979. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : I︠U︡. S. Ilʹi︠a︡shenko
Publisher : American Mathematical Soc.
ISBN 13 : 0821836676
Total Pages : 641 pages
Book Rating : 4.75/5 ( download)

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Download or read book Lectures on Analytic Differential Equations written by I︠U︡. S. Ilʹi︠a︡shenko and published by American Mathematical Soc.. This book was released on 2008 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 mor 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.

Author : Lawrence Markus
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.78/5 ( download)

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Download or read book Group Theory and Differential Equations written by Lawrence Markus and published by . This book was released on 1959 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Witold Hurewicz
Publisher : Courier Corporation
ISBN 13 : 048679721X
Total Pages : 144 pages
Book Rating : 4.12/5 ( download)

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Download or read book Lectures on Ordinary Differential Equations written by Witold Hurewicz and published by Courier Corporation. This book was released on 2014-07-21 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Nail H. Ibragimov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110379503
Total Pages : 198 pages
Book Rating : 4.01/5 ( download)

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Download or read book Tensors and Riemannian Geometry written by Nail H. Ibragimov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-08-31 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the experience of teaching the subject by the author in Russia, France, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics on tensors, Riemannian geometry and geometric approach to partial differential equations. Application of approximate transformation groups to the equations of general relativity in the de Sitter space simplifies the subject significantly.