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Author: Marius van der Put Publisher: Springer Science & Business Media ISBN: 3642557503 Category : Mathematics Languages : en Pages : 438
Book Description
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: Marius van der Put Publisher: Springer Science & Business Media ISBN: 3642557503 Category : Mathematics Languages : en Pages : 438
Book Description
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: Peter Kunkel Publisher: European Mathematical Society ISBN: 9783037190173 Category : Boundary value problems Languages : en Pages : 396
Book Description
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: Werner M. Seiler Publisher: Springer Science & Business Media ISBN: 3642012876 Category : Mathematics Languages : en Pages : 663
Book Description
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: Konstantin Sergeevich Sibirskiĭ Publisher: Manchester University Press ISBN: 9780719026690 Category : Differential equations, Nonlinear Languages : en Pages : 210
Book Description
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: Joseph Fels Ritt Publisher: American Mathematical Soc. ISBN: 0821846388 Category : Mathematics Languages : en Pages : 194
Book Description
A gigantic task undertaken by J. F. Ritt and his collaborators in the 1930's was to give the classical theory of nonlinear differential equations, similar to the theory created by Emmy Noether and her school for algebraic equations and algebraic varieties. The current book presents the results of 20 years of work on this problem. The book quickly became a classic, and thus far, it remains one of the most complete and valuable accounts of differential algebra and its applications.
Author: Li Guo Publisher: World Scientific ISBN: 9789810247034 Category : Mathematics Languages : en Pages : 328
Book Description
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: Norbert Steinmetz Publisher: Springer ISBN: 3319598007 Category : Mathematics Languages : en Pages : 235
Book Description
This book offers a modern introduction to Nevanlinna theory and its intricate relation to the theory of normal families, algebraic functions, asymptotic series, and algebraic differential equations. Following a comprehensive treatment of Nevanlinna’s theory of value distribution, the author presents advances made since Hayman’s work on the value distribution of differential polynomials and illustrates how value- and pair-sharing problems are linked to algebraic curves and Briot–Bouquet differential equations. In addition to discussing classical applications of Nevanlinna theory, the book outlines state-of-the-art research, such as the effect of the Yosida and Zalcman–Pang method of re-scaling to algebraic differential equations, and presents the Painlevé–Yosida theorem, which relates Painlevé transcendents and solutions to selected 2D Hamiltonian systems to certain Yosida classes of meromorphic functions. Aimed at graduate students interested in recent developments in the field and researchers working on related problems, Nevanlinna Theory, Normal Families, and Algebraic Differential Equations will also be of interest to complex analysts looking for an introduction to various topics in the subject area. With examples, exercises and proofs seamlessly intertwined with the body of the text, this book is particularly suitable for the more advanced reader.
Author: Fred Brauer Publisher: Courier Corporation ISBN: 0486151514 Category : Mathematics Languages : en Pages : 325
Book Description
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: Marius van der Put
Author: Marius van der Put
Author: Peter Kunkel
Author: Werner M. Seiler
Author: Konstantin Sergeevich Sibirskiĭ
Author: Joseph Fels Ritt
Author: Malcolm A. H. MacCallum
Author: Li Guo
Author: Norbert Steinmetz
Author: Fred Brauer
Author: Irving Kaplansky