Algebraic Theory Of Differential Equations

Author : Marius van der Put
Publisher : Springer Science & Business Media
ISBN 13 : 3642557503
Total Pages : 446 pages
Book Rating : 4.07/5 ( download)

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Download or read book Galois Theory of Linear Differential Equations written by Marius van der Put and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Konstantin Sergeevich Sibirskiĭ
Publisher : Manchester University Press
ISBN 13 : 9780719026690
Total Pages : 210 pages
Book Rating : 4.95/5 ( download)

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Download or read book Introduction to the Algebraic Theory of Invariants of Differential Equations written by Konstantin Sergeevich Sibirskiĭ and published by Manchester University Press. This book was released on 1988 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Peter Kunkel
Publisher : European Mathematical Society
ISBN 13 : 9783037190173
Total Pages : 396 pages
Book Rating : 4.75/5 ( download)

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Download or read book Differential-algebraic Equations written by Peter Kunkel and published by European Mathematical Society. This book was released on 2006 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential-algebraic equations are a widely accepted tool for the modeling and simulation of constrained dynamical systems in numerous applications, such as mechanical multibody systems, electrical circuit simulation, chemical engineering, control theory, fluid dynamics and many others. This is the first comprehensive textbook that provides a systematic and detailed analysis of initial and boundary value problems for differential-algebraic equations. The analysis is developed from the theory of linear constant coefficient systems via linear variable coefficient systems to general nonlinear systems. Further sections on control problems, generalized inverses of differential-algebraic operators, generalized solutions, and differential equations on manifolds complement the theoretical treatment of initial value problems. Two major classes of numerical methods for differential-algebraic equations (Runge-Kutta and BDF methods) are discussed and analyzed with respect to convergence and order. A chapter is devoted to index reduction methods that allow the numerical treatment of general differential-algebraic equations. The analysis and numerical solution of boundary value problems for differential-algebraic equations is presented, including multiple shooting and collocation methods. A survey of current software packages for differential-algebraic equations completes the text. The book is addressed to graduate students and researchers in mathematics, engineering and sciences, as well as practitioners in industry. A prerequisite is a standard course on the numerical solution of ordinary differential equations. Numerous examples and exercises make the book suitable as a course textbook or for self-study.

Author : Malcolm A. H. MacCallum
Publisher :
ISBN 13 : 9781107367968
Total Pages : 248 pages
Book Rating : 4.64/5 ( download)

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Download or read book Algebraic Theory of Differential Equations written by Malcolm A. H. MacCallum and published by . This book was released on 2009 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique introduction to the subject, reflecting different approaches to the integration of differential equations.

Author : Werner M. Seiler
Publisher : Springer Science & Business Media
ISBN 13 : 3642012876
Total Pages : 663 pages
Book Rating : 4.77/5 ( download)

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Download or read book Involution written by Werner M. Seiler and published by Springer Science & Business Media. This book was released on 2009-10-26 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a self-contained account of the formal theory of general, i.e. also under- and overdetermined, systems of differential equations which in its central notion of involution combines geometric, algebraic, homological and combinatorial ideas.

Author : Li Guo
Publisher : World Scientific
ISBN 13 : 9789810247034
Total Pages : 328 pages
Book Rating : 4.36/5 ( download)

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Download or read book Differential Algebra and Related Topics written by Li Guo and published by World Scientific. This book was released on 2002 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Fred Brauer
Publisher : Courier Corporation
ISBN 13 : 0486151514
Total Pages : 325 pages
Book Rating : 4.19/5 ( download)

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Download or read book The Qualitative Theory of Ordinary Differential Equations written by Fred Brauer and published by Courier Corporation. This book was released on 2012-12-11 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Superb, self-contained graduate-level text covers standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters. Focuses on stability theory and its applications to oscillation phenomena, self-excited oscillations, more. Includes exercises.

Author : Li Guo
Publisher : World Scientific
ISBN 13 : 9814490504
Total Pages : 320 pages
Book Rating : 4.04/5 ( download)

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Download or read book Differential Algebra and Related Topics written by Li Guo and published by World Scientific. This book was released on 2002-05-30 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents:The Ritt–Kolchin Theory for Differential Polynomials (W Y Sit)Differential Schemes (J J Kovacic)Differential Algebra — A Scheme Theory Approach (H Gillet)Model Theory and Differential Algebra (T Scanlon)Inverse Differential Galois Theory (A R Magid)Differential Galois Theory, Universal Rings and Universal Groups (M van der Put)Cyclic Vectors (R C Churchill & J J Kovacic)Differential Algebraic Techniques in Hamiltonian Mechanics (R C Churchill)Moving Frames and Differential Algebra (E L Mansfield)Baxter Algebras and Differential Algebras (L Guo) Readership: Graduate students, pure mathematicians, logicians, algebraic geometers, applied mathematicians and physicists. Keywords:Differential Algebra;Mathematical Logic;Algebraic Geometry;Mathematical Physics

Author : Rafael Martínez-Guerra
Publisher : Springer
ISBN 13 : 3030120252
Total Pages : 196 pages
Book Rating : 4.52/5 ( download)

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Download or read book Algebraic and Differential Methods for Nonlinear Control Theory written by Rafael Martínez-Guerra and published by Springer. This book was released on 2019-01-30 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a short primer in engineering mathematics with a view on applications in nonlinear control theory. In particular, it introduces some elementary concepts of commutative algebra and algebraic geometry which offer a set of tools quite different from the traditional approaches to the subject matter. This text begins with the study of elementary set and map theory. Chapters 2 and 3 on group theory and rings, respectively, are included because of their important relation to linear algebra, the group of invertible linear maps (or matrices) and the ring of linear maps of a vector space. Homomorphisms and Ideals are dealt with as well at this stage. Chapter 4 is devoted to the theory of matrices and systems of linear equations. Chapter 5 gives some information on permutations, determinants and the inverse of a matrix. Chapter 6 tackles vector spaces over a field, Chapter 7 treats linear maps resp. linear transformations, and in addition the application in linear control theory of some abstract theorems such as the concept of a kernel, the image and dimension of vector spaces are illustrated. Chapter 8 considers the diagonalization of a matrix and their canonical forms. Chapter 9 provides a brief introduction to elementary methods for solving differential equations and, finally, in Chapter 10, nonlinear control theory is introduced from the point of view of differential algebra.

Author : Matthias Aschenbrenner
Publisher : Princeton University Press
ISBN 13 : 1400885418
Total Pages : 880 pages
Book Rating : 4.11/5 ( download)

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Download or read book Asymptotic Differential Algebra and Model Theory of Transseries written by Matthias Aschenbrenner and published by Princeton University Press. This book was released on 2017-06-06 with total page 880 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms. Over the last thirty years, transseries emerged variously as super-exact asymptotic expansions of return maps of analytic vector fields, in connection with Tarski's problem on the field of reals with exponentiation, and in mathematical physics. Their formal nature also makes them suitable for machine computations in computer algebra systems. This self-contained book validates the intuition that the differential field of transseries is a universal domain for asymptotic differential algebra. It does so by establishing in the realm of transseries a complete elimination theory for systems of algebraic differential equations with asymptotic side conditions. Beginning with background chapters on valuations and differential algebra, the book goes on to develop the basic theory of valued differential fields, including a notion of differential-henselianity. Next, H-fields are singled out among ordered valued differential fields to provide an algebraic setting for the common properties of Hardy fields and the differential field of transseries. The study of their extensions culminates in an analogue of the algebraic closure of a field: the Newton-Liouville closure of an H-field. This paves the way to a quantifier elimination with interesting consequences.