Approaches To The Qualitative Theory Of Ordinary Differential Equations
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Approaches To The Qualitative Theory Of Ordinary Differential Equations
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Author : Tong-Ren Ding
language : en
Publisher: World Scientific
Release Date : 2007
Approaches To The Qualitative Theory Of Ordinary Differential Equations written by Tong-Ren Ding and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This book is an ideal text for advanced undergraduate students and graduate students with an interest in the qualitative theory of ordinary differential equations and dynamical systems. Elementary knowledge is emphasized by the detailed discussions on the fundamental theorems of the Cauchy problem, fixed-point theorems (especially the twist theorems), the principal idea of dynamical systems, the nonlinear oscillation of Duffing's equation, and some special analyses of particular differential equations. It also contains the latest research by the author as an integral part of the book.
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 Odes An Introduction To Dynamical Systems Theory
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Author : Henryk Zoladek
language : en
Publisher: World Scientific
Release Date : 2022-10-21
Qualitative Theory Of Odes An Introduction To Dynamical Systems Theory written by Henryk Zoladek and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-21 with Mathematics categories.
The Qualitative Theory of Ordinary Differential Equations (ODEs) occupies a rather special position both in Applied and Theoretical Mathematics. On the one hand, it is a continuation of the standard course on ODEs. On the other hand, it is an introduction to Dynamical Systems, one of the main mathematical disciplines in recent decades. Moreover, it turns out to be very useful for graduates when they encounter differential equations in their work; usually those equations are very complicated and cannot be solved by standard methods.The main idea of the qualitative analysis of differential equations is to be able to say something about the behavior of solutions of the equations, without solving them explicitly. Therefore, in the first place such properties like the stability of solutions stand out. It is the stability with respect to changes in the initial conditions of the problem. Note that, even with the numerical approach to differential equations, all calculations are subject to a certain inevitable error. Therefore, it is desirable that the asymptotic behavior of the solutions is insensitive to perturbations of the initial state.Each chapter contains a series of problems (with varying degrees of difficulty) and a self-respecting student should solve them. This book is based on Raul Murillo's translation of Henryk Żołądek's lecture notes, which were in Polish and edited in the portal Matematyka Stosowana (Applied Mathematics) in the University of Warsaw.
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
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.
Methods Of Qualitative Theory Of Differential Equations And Related Topics
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Author : Lev M. Lerman
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Methods Of Qualitative Theory Of Differential Equations And Related Topics written by Lev M. Lerman 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 2000 with Mathematics categories.
Dedicated to the memory of Professor E. A. Leontovich-Andronova, this book was composed by former students and colleagues who wished to mark her contributions to the theory of dynamical systems. A detailed introduction by Leontovich-Andronova's close colleague, L. Shilnikov, presents biographical data and describes her main contribution to the theory of bifurcations and dynamical systems. The main part of the volume is composed of research papers presenting the interests of Leontovich-Andronova, her students and her colleagues. Included are articles on traveling waves in coupled circle maps, bifurcations near a homoclinic orbit, polynomial quadratic systems on the plane, foliations on surfaces, homoclinic bifurcations in concrete systems, topology of plane controllability regions, separatrix cycle with two saddle-foci, dynamics of 4-dimensional symplectic maps, torus maps from strong resonances, structure of 3 degree-of-freedom integrable Hamiltonian systems, splitting separatrices in complex differential equations, Shilnikov's bifurcation for C1-smooth systems and "blue sky catastrophe" for periodic orbits.
The Qualitative Theory Of Ordinary Differential Equations
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Author : Fred Brauer
language : en
Publisher:
Release Date : 1975
The Qualitative Theory Of Ordinary Differential Equations written by Fred Brauer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
Ordinary Differential Equations
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Author : Jane Cronin
language : en
Publisher: CRC Press
Release Date : 1994-02-15
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 1994-02-15 with Mathematics categories.
This text, now in its second edition, presents the basic theory of ordinary differential equations and relates the topological theory used in differential equations to advanced applications in chemistry and biology. It provides new motivations for studying extension theorems and existence theorems, supplies real-world examples, gives an early introduction to the use of geometric methods and offers a novel treatment of the Sturm-Liouville theory.
Ordinary Differential Equations Basic Methods Qualitative Theory And Fun Models
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Author : Michail Zhitomirskii
language : en
Publisher: World Scientific Publishing Company
Release Date : 2024-07-30
Ordinary Differential Equations Basic Methods Qualitative Theory And Fun Models written by Michail Zhitomirskii and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-30 with Mathematics categories.
One of the few books on Ordinary Differential Equations (ODEs), this book contains both qualitative theory, allowing students to analyze the solutions without obtaining formulas, and methods and techniques for obtaining formulas. It features friendly explanations of theorems on top of their formal proofs, expressed in examples, questions, figures, exercises, fun models related to various aspects of life, and even Math Theater explaining, using ODEs, the advantage of optimization by feedback versus a rigid plan. Exercises, both simple and more advanced levels, can be found within.This will allow students to deal with ODEs with a full understanding of what they are doing rather than manipulating with symbols, and even to extend themselves some theorems and techniques. The book is designed for students, teachers, and researchers. It can be used straightforwardly for a one-semester course on ODEs; alternatively, teachers might find it worthwhile to include some of the chapters in their course.
Qualitative Theory Of Differential Equations
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Author : Zhang Zhi-fen
language : en
Publisher: American Mathematical Soc.
Release Date : 2006-07-26
Qualitative Theory Of Differential Equations written by Zhang Zhi-fen 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 2006-07-26 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.