Qualitative Theory Of Odes
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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.
Qualitative Theory Of Odes
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Author : Henryk Żołądek
language : en
Publisher:
Release Date : 2022
Qualitative Theory Of Odes written by Henryk Żołądek and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Differential equations 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 the first author's translation of lecture notes in Polish by the second author, edited in the portal Matematyka Stosowana (Applied Mathematics) at the University of Warsaw"--
The Qualitative Theory Of Ordinary Differential Equations
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Author : Fred Brauer
language : en
Publisher: Courier Corporation
Release Date : 1989-01-01
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 1989-01-01 with Mathematics categories.
"This is a very good book ... with many well-chosen examples and illustrations." — American Mathematical Monthly This highly regarded text presents a self-contained introduction to some important aspects of modern qualitative theory for ordinary differential equations. It is accessible to any student of physical sciences, mathematics or engineering who has a good knowledge of calculus and of the elements of linear algebra. In addition, algebraic results are stated as needed; the less familiar ones are proved either in the text or in appendixes. The topics covered in the first three chapters are the standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters. The next three chapters, the heart of the book, deal with stability theory and some applications, such as oscillation phenomena, self-excited oscillations and the regulator problem of Lurie. One of the special features of this work is its abundance of exercises-routine computations, completions of mathematical arguments, extensions of theorems and applications to physical problems. Moreover, they are found in the body of the text where they naturally occur, offering students substantial aid in understanding the ideas and concepts discussed. The level is intended for students ranging from juniors to first-year graduate students in mathematics, physics or engineering; however, the book is also ideal for a one-semester undergraduate course in ordinary differential equations, or for engineers in need of a course in state space methods.
Ordinary Differential Equations Basics And Beyond
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Author : David G. Schaeffer
language : en
Publisher: Springer
Release Date : 2016-11-10
Ordinary Differential Equations Basics And Beyond written by David G. Schaeffer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-10 with Mathematics categories.
This book develops the theory of ordinary differential equations (ODEs), starting from an introductory level (with no prior experience in ODEs assumed) through to a graduate-level treatment of the qualitative theory, including bifurcation theory (but not chaos). While proofs are rigorous, the exposition is reader-friendly, aiming for the informality of face-to-face interactions. A unique feature of this book is the integration of rigorous theory with numerous applications of scientific interest. Besides providing motivation, this synthesis clarifies the theory and enhances scientific literacy. Other features include: (i) a wealth of exercises at various levels, along with commentary that explains why they matter; (ii) figures with consistent color conventions to identify nullclines, periodic orbits, stable and unstable manifolds; and (iii) a dedicated website with software templates, problem solutions, and other resources supporting the text (www.math.duke.edu/ode-book). Given its many applications, the book may be used comfortably in science and engineering courses as well as in mathematics courses. Its level is accessible to upper-level undergraduates but still appropriate for graduate students. The thoughtful presentation, which anticipates many confusions of beginning students, makes the book suitable for a teaching environment that emphasizes self-directed, active learning (including the so-called inverted classroom).
Non Linear Analysis And Boundary Value Problems For Ordinary Differential Equations
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Author : F. Zanolin
language : en
Publisher: Springer
Release Date : 2014-05-04
Non Linear Analysis And Boundary Value Problems For Ordinary Differential Equations written by F. Zanolin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-04 with Technology & Engineering categories.
The area covered by this volume represents a broad choice of some interesting research topics in the field of dynamical systems and applications of nonlinear analysis to ordinary and partial differential equations. The contributed papers, written by well known specialists, make this volume a useful tool both for the experts (who can find recent and new results) and for those who are interested in starting a research work in one of these topics (who can find some updated and carefully presented papers on the state of the art of the corresponding subject).
Ordinary Differential Equations
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Author : David A. Sanchez
language : en
Publisher: American Mathematical Soc.
Release Date : 2002-12-31
Ordinary Differential Equations written by David A. Sanchez 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 2002-12-31 with Mathematics categories.
For the instructor or student confronting an introductory course in ordinary differential equations there is a need for a brief guide to the key concepts in the subject. Important topics like stability, resonance, existence of periodic solutions, and the essential role of continuation of solutions are often engulfed in a sea of exercises in integration, linear algebra theory, computer programming and an overdose of series expansions. This book is intended as that guide. It is more conceptual than definitive and more light-hearted than pedagogic. It covers key topics and theoretical underpinnings that are necessary for the study of rich topics like nonlinear equations or stability theory. The [Author]; has included a great many illuminating examples and discussions that uncover the conceptual heart of the matter.
Qualitative Simulation Modeling And Analysis
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Author : Paul A. Fishwick
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Qualitative Simulation Modeling And Analysis written by Paul A. Fishwick 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 2012-12-06 with Computers categories.
Recently there has been considerable interest in qualitative methods in simulation and mathematical model- ing. Qualitative Simulation Modeling and Analysis is the first book to thoroughly review fundamental concepts in the field of qualitative simulation. The book will appeal to readers in a variety of disciplines including researchers in simulation methodology, artificial intelligence and engineering. This book boldly attempts to bring together, for the first time, the qualitative techniques previously found only in hard-to-find journals dedicated to single disciplines. The book is written for scientists and engineers interested in improving their knowledge of simulation modeling. The "qualitative" nature of the book stresses concepts of invariance, uncertainty and graph-theoretic bases for modeling and analysis.
A Short Course In Ordinary Differential Equations
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Author : Qingkai Kong
language : en
Publisher: Springer
Release Date : 2014-10-21
A Short Course In Ordinary Differential Equations written by Qingkai Kong and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-21 with Mathematics categories.
This text is a rigorous treatment of the basic qualitative theory of ordinary differential equations, at the beginning graduate level. Designed as a flexible one-semester course but offering enough material for two semesters, A Short Course covers core topics such as initial value problems, linear differential equations, Lyapunov stability, dynamical systems and the Poincaré—Bendixson theorem, and bifurcation theory, and second-order topics including oscillation theory, boundary value problems, and Sturm—Liouville problems. The presentation is clear and easy-to-understand, with figures and copious examples illustrating the meaning of and motivation behind definitions, hypotheses, and general theorems. A thoughtfully conceived selection of exercises together with answers and hints reinforce the reader's understanding of the material. Prerequisites are limited to advanced calculus and the elementary theory of differential equations and linear algebra, making the text suitable for senior undergraduates as well.
An Introduction To Semiflows
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Author : Albert J. Milani
language : en
Publisher: CRC Press
Release Date : 2004-10-14
An Introduction To Semiflows written by Albert J. Milani and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-14 with Mathematics categories.
This book introduces the class of dynamical systems called semiflows, which includes systems defined or modeled by certain types of differential evolution equations (DEEs). It focuses on the basic results of the theory of dynamical systems that can be extended naturally and applied to study the asymptotic behavior of the solutions of DEEs. The auth
Handbook Of Differential Equations Ordinary Differential Equations
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Author : A. Canada
language : en
Publisher: Elsevier
Release Date : 2006-08-21
Handbook Of Differential Equations Ordinary Differential Equations written by A. Canada and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-21 with Mathematics categories.
This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience. These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for reseach, learing and teaching. This volumes consists of seven chapters covering a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume. - Covers a variety of problems in ordinary differential equations - Pure mathematical and real world applications - Written for mathematicians and scientists of many related fields