A First Course In The Qualitative Theory Of Differential Equations
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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.
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 Planar Differential Systems
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Author : Freddy Dumortier
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-10-13
Qualitative Theory Of Planar Differential Systems written by Freddy Dumortier 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 2006-10-13 with Mathematics categories.
This book deals with systems of polynomial autonomous ordinary differential equations in two real variables. The emphasis is mainly qualitative, although attention is also given to more algebraic aspects as a thorough study of the center/focus problem and recent results on integrability. In the last two chapters the performant software tool P4 is introduced. From the start, differential systems are represented by vector fields enabling, in full strength, a dynamical systems approach. All essential notions, including invariant manifolds, normal forms, desingularization of singularities, index theory and limit cycles, are introduced and the main results are proved for smooth systems with the necessary specifications for analytic and polynomial systems.
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.
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
Differential Equations And Their Applications
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Author : M. Braun
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Differential Equations And Their Applications written by M. Braun 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 Mathematics categories.
This textbook is a unique blend of the theory of differential equations and their exciting application to "real world" problems. First, and foremost, it is a rigorous study of ordinary differential equations and can be fully un derstood by anyone who has completed one year of calculus. However, in addition to the traditional applications, it also contains many exciting "real life" problems. These applications are completely self contained. First, the problem to be solved is outlined clearly, and one or more differential equa tions are derived as a model for this problem. These equations are then solved, and the results are compared with real world data. The following applications are covered in this text. I. In Section 1.3 we prove that the beautiful painting "Disciples of Emmaus" which was bought by the Rembrandt Society of Belgium for $170,000 was a modem forgery. 2. In Section 1.5 we derive differential equations which govern the population growth of various species, and compare the results predicted by our models with the known values of the populations. 3. In Section 1.6 we derive differential equations which govern the rate at which farmers adopt new innovations. Surprisingly, these same differen tial equations govern the rate at which technological innovations are adopted in such diverse industries as coal, iron and steel, brewing, and railroads.
Differential Equations
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Author : Jane Cronin
language : en
Publisher:
Release Date : 1980
Differential Equations written by Jane Cronin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
Existence theorems; Linear systems; Autonomous systems; Stability; The lyapunov second method; Periodic solutions; Bifurcation and branching of periodic solutions.
The Theory Of Differential Equations
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Author : Walter G. Kelley
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-04-22
The Theory Of Differential Equations written by Walter G. Kelley 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 2010-04-22 with Mathematics categories.
For over 300 years, differential equations have served as an essential tool for describing and analyzing problems in many scientific disciplines. This carefully-written textbook provides an introduction to many of the important topics associated with ordinary differential equations. Unlike most textbooks on the subject, this text includes nonstandard topics such as perturbation methods and differential equations and Mathematica. In addition to the nonstandard topics, this text also contains contemporary material in the area as well as its classical topics. This second edition is updated to be compatible with Mathematica, version 7.0. It also provides 81 additional exercises, a new section in Chapter 1 on the generalized logistic equation, an additional theorem in Chapter 2 concerning fundamental matrices, and many more other enhancements to the first edition. This book can be used either for a second course in ordinary differential equations or as an introductory course for well-prepared students. The prerequisites for this book are three semesters of calculus and a course in linear algebra, although the needed concepts from linear algebra are introduced along with examples in the book. An undergraduate course in analysis is needed for the more theoretical subjects covered in the final two chapters.
A First Course In Ordinary Differential Equations
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Author : Suman Kumar Tumuluri
language : en
Publisher: CRC Press
Release Date : 2021-03-26
A First Course In Ordinary Differential Equations written by Suman Kumar Tumuluri and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-26 with Mathematics categories.
A First course in Ordinary Differential Equations provides a detailed introduction to the subject focusing on analytical methods to solve ODEs and theoretical aspects of analyzing them when it is difficult/not possible to find their solutions explicitly. This two-fold treatment of the subject is quite handy not only for undergraduate students in mathematics but also for physicists, engineers who are interested in understanding how various methods to solve ODEs work. More than 300 end-of-chapter problems with varying difficulty are provided so that the reader can self examine their understanding of the topics covered in the text. Most of the definitions and results used from subjects like real analysis, linear algebra are stated clearly in the book. This enables the book to be accessible to physics and engineering students also. Moreover, sufficient number of worked out examples are presented to illustrate every new technique introduced in this book. Moreover, the author elucidates the importance of various hypotheses in the results by providing counter examples. Features Offers comprehensive coverage of all essential topics required for an introductory course in ODE. Emphasizes on both computation of solutions to ODEs as well as the theoretical concepts like well-posedness, comparison results, stability etc. Systematic presentation of insights of the nature of the solutions to linear/non-linear ODEs. Special attention on the study of asymptotic behavior of solutions to autonomous ODEs (both for scalar case and 2✕2 systems). Sufficient number of examples are provided wherever a notion is introduced. Contains a rich collection of problems. This book serves as a text book for undergraduate students and a reference book for scientists and engineers. Broad coverage and clear presentation of the material indeed appeals to the readers. Dr. Suman K. Tumuluri has been working in University of Hyderabad, India, for 11 years and at present he is an associate professor. His research interests include applications of partial differential equations in population dynamics and fluid dynamics.
Regular Variation And Differential Equations
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Author : Vojislav Maric
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-03-27
Regular Variation And Differential Equations written by Vojislav Maric 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 2000-03-27 with Mathematics categories.
This book constitutes the refereed proceedings of the Third Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD '99, held in Beijing, China, in April 1999. The 29 revised full papers presented together with 37 short papers were carefully selected from a total of 158 submissions. The book is divided into sections on emerging KDD technology; association rules; feature selection and generation; mining in semi-unstructured data; interestingness, surprisingness, and exceptions; rough sets, fuzzy logic, and neural networks; induction, classification, and clustering; visualization; causal models and graph-based methods; agent-based and distributed data mining; and advanced topics and new methodologies.