Qualitative Theory Of Differential Equations
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The Qualitative Theory Of Ordinary Differential Equations
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Author : Fred Brauer
language : en
Publisher: Courier Corporation
Release Date : 2012-12-11
The Qualitative Theory Of Ordinary Differential Equations written by Fred Brauer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-11 with Mathematics categories.
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.
Qualitative Theory Of Differential Equations
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Author : Miklós Farkas
language : en
Publisher: North Holland
Release Date : 1981
Qualitative Theory Of Differential Equations written by Miklós Farkas and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
A First Course In The Qualitative Theory Of Differential Equations
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Author : James Hetao Liu
language : en
Publisher:
Release Date : 2003
A First Course In The Qualitative Theory Of Differential Equations written by James Hetao Liu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Juvenile Nonfiction categories.
This book provides a complete analysis of those subjects that are of fundamental importance to the qualitative theory of differential equations and related to current research-including details that other books in the field tend to overlook. Chapters 1-7 cover the basic qualitative properties concerning existence and uniqueness, structures of solutions, phase portraits, stability, bifurcation and chaos. Chapters 8-12 cover stability, dynamical systems, and bounded and periodic solutions. A good reference book for teachers, researchers, and other professionals.
Qualitative Theory Of Differential Equations
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Author : Zhifen Zhang
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Qualitative Theory Of Differential Equations written by Zhifen Zhang 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 1992 with Mathematics categories.
Subriemannian geometries, also known as Carnot-Caratheodory geometries, can be viewed as limits of Riemannian geometries. They also arise in physical phenomenon involving ``geometric phases'' or holonomy. Very roughly speaking, a subriemannian geometry consists of a manifold endowed with a distribution (meaning a $k$-plane field, or subbundle of the tangent bundle), called horizontal together with an inner product on that distribution. If $k=n$, the dimension of the manifold, we get the usual Riemannian geometry. Given a subriemannian geometry, we can define the distance between two points just as in the Riemannian case, except we are only allowed to travel along the horizontal lines between two points. The book is devoted to the study of subriemannian geometries, their geodesics, and their applications. It starts with the simplest nontrivial example of a subriemannian geometry: the two-dimensional isoperimetric problem reformulated as a problem of finding subriemannian geodesics. Among topics discussed in other chapters of the first part of the book the author mentions an elementary exposition of Gromov's surprising idea to use subriemannian geometry for proving a theorem in discrete group theory and Cartan's method of equivalence applied to the problem of understanding invariants (diffeomorphism types) of distributions. There is also a chapter devoted to open problems. The second part of the book is devoted to applications of subriemannian geometry. In particular, the author describes in detail the following four physical problems: Berry's phase in quantum mechanics, the problem of a falling cat righting herself, that of a microorganism swimming, and a phase problem arising in the $N$-body problem. He shows that all these problems can be studied using the same underlying type of subriemannian geometry: that of a principal bundle endowed with $G$-invariant metrics. Reading the book requires introductory knowledge of differential geometry, and it can serve as a good introduction to this new, exciting area of mathematics. This book provides an introduction to and a comprehensive study of the qualitative theory of ordinary differential equations. It begins with fundamental theorems on existence, uniqueness, and initial conditions, and discusses basic principles in dynamical systems and Poincare-Bendixson theory. The authors present a careful analysis of solutions near critical points of linear and nonlinear planar systems and discuss indices of planar critical points. A very thorough study of limit cycles is given, including many results on quadratic systems and recent developments in China. Other topics included are: the critical point at infinity, harmonic solutions for periodic differential equations, systems of ordinary differential equations on the torus, and structural stability for systems on two-dimensional manifolds. This books is accessible to graduate students and advanced undergraduates and is also of interest to researchers in this area. Exercises are included at the end of each chapter.
Qualitative Theory Of Differential Equations
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Author : Viktor Vladimirovich Nemytskii
language : en
Publisher:
Release Date : 1960
Qualitative Theory Of Differential Equations written by Viktor Vladimirovich Nemytskii and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with categories.
Qualitative Theory Of Differential Equations
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Author : Viktor Vladimirovich Nemytskii
language : en
Publisher: Princeton University Press
Release Date : 2015-12-08
Qualitative Theory Of Differential Equations written by Viktor Vladimirovich Nemytskii and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-08 with Mathematics categories.
Book 22 in the Princeton Mathematical Series. Originally published in 1960. 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.
Introduction To The Qualitative Theory Of Differential Systems
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Author : Jaume Llibre
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-30
Introduction To The Qualitative Theory Of Differential Systems written by Jaume Llibre 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 2013-10-30 with Mathematics categories.
The book deals with continuous piecewise linear differential systems in the plane with three pieces separated by a pair of parallel straight lines. Moreover, these differential systems are symmetric with respect to the origin of coordinates. This class of systems driven by concrete applications is of interest in engineering, in particular in control theory and the design of electric circuits. By studying these particular differential systems we will introduce the basic tools of the qualitative theory of ordinary differential equations, which allow us to describe the global dynamics of these systems including the infinity. The behavior of their solutions, their parametric stability or instability and their bifurcations are described. The book is very appropriate for a first course in the qualitative theory of differential equations or dynamical systems, mainly for engineers, mathematicians, and physicists.
Qualitative Theory Of Differential Equations By V V Nemytskii And V V Stepanov
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Author : Viktor Vladimirovich Nemyt︠s︡kiĭ
language : en
Publisher:
Release Date :
Qualitative Theory Of Differential Equations By V V Nemytskii And V V Stepanov written by Viktor Vladimirovich Nemyt︠s︡kiĭ and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Differential equations categories.
Ordinary Differential Equations
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Author : Luis Barreira
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-06-06
Ordinary Differential Equations written by Luis Barreira 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 2012-06-06 with Mathematics categories.
This textbook provides a comprehensive introduction to the qualitative theory of ordinary differential equations. It includes a discussion of the existence and uniqueness of solutions, phase portraits, linear equations, stability theory, hyperbolicity and equations in the plane. The emphasis is primarily on results and methods that allow one to analyze qualitative properties of the solutions without solving the equations explicitly. The text includes numerous examples that illustrate in detail the new concepts and results as well as exercises at the end of each chapter. The book is also intended to serve as a bridge to important topics that are often left out of a course on ordinary differential equations. In particular, it provides brief introductions to bifurcation theory, center manifolds, normal forms and Hamiltonian systems.
Ordinary Differential Equations
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Author : Jane Cronin
language : en
Publisher: CRC Press
Release Date : 2007-12-14
Ordinary Differential Equations written by Jane Cronin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-14 with Mathematics categories.
Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of