Algebraic Theory Of Differential Equations

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Galois Theory Of Linear Differential Equations

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Author : Marius van der Put
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-01-21

Galois Theory Of Linear Differential Equations written by Marius van der Put and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-21 with Mathematics categories.

From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews

Algebraic Theory Of Differential Equations

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Author :
language : en
Publisher: Cambridge University Press
Release Date :

Algebraic Theory Of Differential Equations written by and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Algebraic Theory Of Differential Equations

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Author : Malcolm A. H. MacCallum
language : en
Publisher:
Release Date : 2009

Algebraic Theory Of Differential Equations written by Malcolm A. H. MacCallum and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Algebraic number theory categories.

A unique introduction to the subject, reflecting different approaches to the integration of differential equations.

The Geometric Theory Of Ordinary Differential Equations And Algebraic Functions

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Author : Georges Valiron
language : en
Publisher: Math Science Press
Release Date : 1984

The Geometric Theory Of Ordinary Differential Equations And Algebraic Functions written by Georges Valiron and has been published by Math Science Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.

Introduction To The Algebraic Theory Of Invariants Of Differential Equations

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Author : Konstantin Sergeevich Sibirskiĭ
language : en
Publisher: Manchester University Press
Release Date : 1988

Introduction To The Algebraic Theory Of Invariants Of Differential Equations written by Konstantin Sergeevich Sibirskiĭ and has been published by Manchester University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.

Considers polynominal invariants & comitants of autonomous systems of differential equations with right-hand sides relative to various transformation groups of phase space. Contains an in-depth discussion of the two-dimensional system with quadratic right-hand sides. Features numerous applications to the qualitative theory of differential equations.

Algebraic Theory Of Differential Equations

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Author : Thomas J. Little
language : en
Publisher:
Release Date : 1999

Algebraic Theory Of Differential Equations written by Thomas J. Little and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Differential equations categories.

Differential Algebra And Related Topics Proceedings Of The International Workshop

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Author : Phyllis J Cassidy
language : en
Publisher: World Scientific
Release Date : 2002-05-30

Differential Algebra And Related Topics Proceedings Of The International Workshop written by Phyllis J Cassidy and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-30 with Mathematics categories.

Differential algebra explores properties of solutions to systems of (ordinary or partial, linear or nonlinear) differential equations from an algebraic point of view. It includes as special cases algebraic systems as well as differential systems with algebraic constraints. This algebraic theory of Joseph F Ritt and Ellis R Kolchin is further enriched by its interactions with algebraic geometry, Diophantine geometry, differential geometry, model theory, control theory, automatic theorem proving, combinatorics, and difference equations. Differential algebra now plays an important role in computational methods such as symbolic integration, and symmetry analysis of differential equations. This volume includes tutorial and survey papers presented at workshop.

Differential Galois Theory Through Riemann Hilbert Correspondence

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Author : Jacques Sauloy
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-12-07

Differential Galois Theory Through Riemann Hilbert Correspondence written by Jacques Sauloy and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-07 with Mathematics categories.

Differential Galois theory is an important, fast developing area which appears more and more in graduate courses since it mixes fundamental objects from many different areas of mathematics in a stimulating context. For a long time, the dominant approach, usually called Picard-Vessiot Theory, was purely algebraic. This approach has been extensively developed and is well covered in the literature. An alternative approach consists in tagging algebraic objects with transcendental information which enriches the understanding and brings not only new points of view but also new solutions. It is very powerful and can be applied in situations where the Picard-Vessiot approach is not easily extended. This book offers a hands-on transcendental approach to differential Galois theory, based on the Riemann-Hilbert correspondence. Along the way, it provides a smooth, down-to-earth introduction to algebraic geometry, category theory and tannakian duality. Since the book studies only complex analytic linear differential equations, the main prerequisites are complex function theory, linear algebra, and an elementary knowledge of groups and of polynomials in many variables. A large variety of examples, exercises, and theoretical constructions, often via explicit computations, offers first-year graduate students an accessible entry into this exciting area.

Differential Algebra And Related Topics

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Author : Li Guo
language : en
Publisher: World Scientific
Release Date : 2002

Differential Algebra And Related Topics written by Li Guo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

Differential algebra explores properties of solutions of systems of (ordinary or partial, linear or non-linear) differential equations from an algebraic point of view. It includes as special cases algebraic systems as well as differential systems with algebraic constraints. This algebraic theory of Joseph F Ritt and Ellis R Kolchin is further enriched by its interactions with algebraic geometry, Diophantine geometry, differential geometry, model theory, control theory, automatic theorem proving, combinatorics, and difference equations. Differential algebra now plays an important role in computational methods such as symbolic integration and symmetry analysis of differential equations. These proceedings consist of tutorial and survey papers presented at the Second International Workshop on Differential Algebra and Related Topics at Rutgers University, Newark in April 2007. As a sequel to the proceedings of the First International Workshop, this volume covers more related subjects, and provides a modern and introductory treatment to many facets of differential algebra, including surveys of known results, open problems, and new, emerging, directions of research. It is therefore an excellent companion and reference text for graduate students and researchers.

Differential Equations From The Algebraic Standpoint

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Author : Joseph Fels Ritt
language : en
Publisher: American Mathematical Soc.
Release Date : 1932-12-31

Differential Equations From The Algebraic Standpoint written by Joseph Fels Ritt and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1932-12-31 with Mathematics categories.

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).