Implicit First Order Dynamical Systems (II) PDF Download
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Author: Virgil Obădeanu
Publisher:
ISBN:
Category : Differentiable dynamical systems
Languages : en
Pages : 18
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Book Description
Author: Virgil Obădeanu
Publisher:
ISBN:
Category : Differentiable dynamical systems
Languages : en
Pages : 18
Get Book Here
Book Description
Author: Virgil Obădeanu
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
Author: Virgil Obădeanu
Publisher:
ISBN:
Category : Differentiable dynamical systems
Languages : en
Pages : 14
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Book Description
Author: Virgil Obădeanu
Publisher:
ISBN:
Category : Differentiable dynamical systems
Languages : en
Pages : 26
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Book Description
Author: Gerald Teschl
Publisher: American Mathematical Society
ISBN: 147047641X
Category : Mathematics
Languages : en
Pages : 370
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Book Description
This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm–Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincaré–Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman–Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale–Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.
Author: Andrew Stuart
Publisher: Cambridge University Press
ISBN: 9780521645638
Category : Mathematics
Languages : en
Pages : 708
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Book Description
The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems and the convergence and stability properties of the methods are examined.
Author: Virgil Obădeanu
Publisher:
ISBN:
Category : Differentiable dynamical systems
Languages : en
Pages : 12
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Book Description
Author: Virgil Obădeanu
Publisher:
ISBN:
Category : Differentiable dynamical systems
Languages : en
Pages : 14
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Book Description
Author: Lawrence Perko
Publisher: Springer Science & Business Media
ISBN: 1468402498
Category : Mathematics
Languages : en
Pages : 530
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Book Description
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence bf interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mat!!ematics (TAM). The development of new courses is a natural consequence of a high level of excitement oil the research frontier as newer techniques, such as numerical and symbolic cotnputer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Math ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface to the Second Edition This book covers those topics necessary for a clear understanding of the qualitative theory of ordinary differential equations and the concept of a dynamical system. It is written for advanced undergraduates and for beginning graduate students. It begins with a study of linear systems of ordinary differential equations, a topic already familiar to the student who has completed a first course in differential equations.
Author: Virginia W. Noonburg
Publisher: American Mathematical Soc.
ISBN: 1470463296
Category : Education
Languages : en
Pages : 402
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Book Description
A thoroughly modern textbook for the sophomore-level differential equations course. The examples and exercises emphasize modeling not only in engineering and physics but also in applied mathematics and biology. There is an early introduction to numerical methods and, throughout, a strong emphasis on the qualitative viewpoint of dynamical systems. Bifurcations and analysis of parameter variation is a persistent theme. Presuming previous exposure to only two semesters of calculus, necessary linear algebra is developed as needed. The exposition is very clear and inviting. The book would serve well for use in a flipped-classroom pedagogical approach or for self-study for an advanced undergraduate or beginning graduate student. This second edition of Noonburg's best-selling textbook includes two new chapters on partial differential equations, making the book usable for a two-semester sequence in differential equations. It includes exercises, examples, and extensive student projects taken from the current mathematical and scientific literature.
