Introduction to Differential Equations and Dynamical Systems

Introduction to Differential Equations and Dynamical Systems

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  • Author: Richard E. Williamson
  • Publisher: McGraw-Hill Science, Engineering & Mathematics
  • ISBN:
  • Category : Differentiable dynamical systems
  • Languages : en
  • Pages : 712

This textbook offers a foundation for a first course in differential equations, covering traditional areas in addition to topics such as dynamical systems. Numerical methods and problem-solving techniques are emphasized throughout the text. Discussion of computer use (Mathematica and Maple) is also included where appropriate, and where individual exercises are marked with an icon, they are best solved with the help of a computer or calculator.


Introduction to Differential Equations with Dynamical Systems

Introduction to Differential Equations with Dynamical Systems

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  • Author: Stephen L. Campbell
  • Publisher: Princeton University Press
  • ISBN: 0691124744
  • Category : Mathematics
  • Languages : en
  • Pages : 446

Many textbooks on differential equations are written to be interesting to the teacher rather than the student. Introduction to Differential Equations with Dynamical Systems is directed toward students. This concise and up-to-date textbook addresses the challenges that undergraduate mathematics, engineering, and science students experience during a first course on differential equations. And, while covering all the standard parts of the subject, the book emphasizes linear constant coefficient equations and applications, including the topics essential to engineering students. Stephen Campbell and Richard Haberman--using carefully worded derivations, elementary explanations, and examples, exercises, and figures rather than theorems and proofs--have written a book that makes learning and teaching differential equations easier and more relevant. The book also presents elementary dynamical systems in a unique and flexible way that is suitable for all courses, regardless of length.


Differential Equations, Dynamical Systems, and Linear Algebra

Differential Equations, Dynamical Systems, and Linear Algebra

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  • Author: Morris W. Hirsch
  • Publisher: Academic Press
  • ISBN: 0080873766
  • Category : Mathematics
  • Languages : en
  • Pages : 358

This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.


Differential Dynamical Systems

Differential Dynamical Systems

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  • Author: James D. Meiss
  • Publisher: SIAM
  • ISBN: 0898716357
  • Category : Mathematics
  • Languages : en
  • Pages : 427

Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems conceptsflow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems. Audience This textbook is intended for senior undergraduates and first-year graduate students in pure and applied mathematics, engineering, and the physical sciences. Readers should be comfortable with elementary differential equations and linear algebra and should have had exposure to advanced calculus. Contents List of Figures; Preface; Acknowledgments; Chapter 1: Introduction; Chapter 2: Linear Systems; Chapter 3: Existence and Uniqueness; Chapter 4: Dynamical Systems; Chapter 5: Invariant Manifolds; Chapter 6: The Phase Plane; Chapter 7: Chaotic Dynamics; Chapter 8: Bifurcation Theory; Chapter 9: Hamiltonian Dynamics; Appendix: Mathematical Software; Bibliography; Index


An Introduction to Dynamical Systems

An Introduction to Dynamical Systems

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  • Author: Rex Clark Robinson
  • Publisher: American Mathematical Soc.
  • ISBN: 0821891359
  • Category : Mathematics
  • Languages : en
  • Pages : 763

This book gives a mathematical treatment of the introduction to qualitative differential equations and discrete dynamical systems. The treatment includes theoretical proofs, methods of calculation, and applications. The two parts of the book, continuous time of differential equations and discrete time of dynamical systems, can be covered independently in one semester each or combined together into a year long course. The material on differential equations introduces the qualitative or geometric approach through a treatment of linear systems in any dimension. There follows chapters where equilibria are the most important feature, where scalar (energy) functions is the principal tool, where periodic orbits appear, and finally, chaotic systems of differential equations. The many different approaches are systematically introduced through examples and theorems. The material on discrete dynamical systems starts with maps of one variable and proceeds to systems in higher dimensions. The treatment starts with examples where the periodic points can be found explicitly and then introduces symbolic dynamics to analyze where they can be shown to exist but not given in explicit form. Chaotic systems are presented both mathematically and more computationally using Lyapunov exponents. With the one-dimensional maps as models, the multidimensional maps cover the same material in higher dimensions. This higher dimensional material is less computational and more conceptual and theoretical. The final chapter on fractals introduces various dimensions which is another computational tool for measuring the complexity of a system. It also treats iterated function systems which give examples of complicated sets. In the second edition of the book, much of the material has been rewritten to clarify the presentation. Also, some new material has been included in both parts of the book. This book can be used as a textbook for an advanced undergraduate course on ordinary differential equations and/or dynamical systems. Prerequisites are standard courses in calculus (single variable and multivariable), linear algebra, and introductory differential equations.


Differential Equations and Dynamical Systems

Differential Equations and Dynamical Systems

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  • Author: D. Bahuguna
  • Publisher: Alpha Science Int'l Ltd.
  • ISBN: 9788173195884
  • Category : Mathematics
  • Languages : en
  • Pages : 246

Fifteen chapters from eminent researchers working in the area of differential equations and dynamical systems covering all relevant subjects, ranging from wavelets and their applications, to second order evolution equations.


Introduction to Differential Equations with Dynamical Systems

Introduction to Differential Equations with Dynamical Systems

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  • Author: Stephen L. Campbell
  • Publisher: Princeton University Press
  • ISBN: 1400841321
  • Category : Mathematics
  • Languages : en
  • Pages : 445

Many textbooks on differential equations are written to be interesting to the teacher rather than the student. Introduction to Differential Equations with Dynamical Systems is directed toward students. This concise and up-to-date textbook addresses the challenges that undergraduate mathematics, engineering, and science students experience during a first course on differential equations. And, while covering all the standard parts of the subject, the book emphasizes linear constant coefficient equations and applications, including the topics essential to engineering students. Stephen Campbell and Richard Haberman--using carefully worded derivations, elementary explanations, and examples, exercises, and figures rather than theorems and proofs--have written a book that makes learning and teaching differential equations easier and more relevant. The book also presents elementary dynamical systems in a unique and flexible way that is suitable for all courses, regardless of length.


Ordinary Differential Equations and Dynamical Systems

Ordinary Differential Equations and Dynamical Systems

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  • Author: Gerald Teschl
  • Publisher: American Mathematical Society
  • ISBN: 147047641X
  • Category : Mathematics
  • Languages : en
  • Pages : 370

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.


Nonlinear Ordinary Differential Equations

Nonlinear Ordinary Differential Equations

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  • Author: Dominic William Jordan
  • Publisher: Oxford University Press, USA
  • ISBN: 9780198565628
  • Category : Mathematics
  • Languages : en
  • Pages : 564

This edition has been completely revised to bring it into line with current teaching, including an expansion of the material on bifurcations and chaos.


Differential Dynamical Systems, Revised Edition

Differential Dynamical Systems, Revised Edition

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  • Author: James D. Meiss
  • Publisher: SIAM
  • ISBN: 161197464X
  • Category : Mathematics
  • Languages : en
  • Pages : 392

Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.? Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple?, Mathematica?, and MATLAB? software to give students practice with computation applied to dynamical systems problems.