We hope this content on epidemiology, disease modeling, pandemics and vaccines will help in the rapid fight against this global problem. Click on title above or here to access this collection. On one level, this text can be viewed as suitable for a traditional course on ordinary differential equations ODEs. Since differential equations are the basis for models of any physical systems that exhibit smooth change, students in all areas of the mathematical sciences and engineering require the tools to understand the methods for solving these equations. It is traditional for this exposure to start during the second year of training in calculus, where the basic methods of solving one- and two-dimensional primarily linear ODEs are studied.

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We hope this content on epidemiology, disease modeling, pandemics and vaccines will help in the rapid fight against this global problem. Click on title above or here to access this collection. 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. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics.

On one level, this text can be viewed as suitable for a traditional course on ordinary differential equations ODEs. Since differential equations are the basis for models of any physical systems that exhibit smooth change, students in all areas of the mathematical sciences and engineering require the tools to understand the methods for solving these equations.

It is traditional for this exposure to start during the second year of training in calculus, where the basic methods of solving one- and two-dimensional primarily linear ODEs are studied. The material for this text has been developed over a decade in a course given to upper-division undergraduates and beginning graduate students in applied mathematics, engineering, and physics at the University of Colorado.

In a one-semester course, I typically cover most of the material in Chapters 1—6 and add a selection of sections from later chapters. There are a number of classic texts for a traditional differential equations course, for example Coddington and Levinson ; Hirsch and Smale ; Hartman Such courses usually begin with a study of linear systems; we begin there as well in Chapter 2.

Matrix algebra is fundamental to this treatment, so we give a brief discussion of eigenvector methods and an extensive treatment of the matrix exponential.

The next stage in the traditional course is to provide a foundation for the study of nonlinear differential equations by showing that, under certain conditions, these equations have solutions existence and that there is only one solution that satisfies a given initial condition uniqueness.

The theoretical underpinning of this result, as well as many other results in applied mathematics, is the majestic contraction mapping theorem. Chapter 3 provides a self-contained introduction to the analytic foundations needed to understand this theorem.

Once this tool is concretely understood, students see that many proofs quickly yield to its power. Sign in Help View Cart. Manage this Book. Add to my favorites. Recommend to Library. Email to a friend. Digg This. Notify Me! E-mail Alerts. RSS Feeds. Title Information. Buy the Print Edition.

Author s : James D. James D. Meiss : University of Colorado, Boulder, Colorado. Keywords: ordinary differential equations , dynamical systems , chaos , nonlinearity , bifurcation , phase space. Return to All Sections. Front Matter. Linear Systems. Existence and Uniqueness. Dynamical Systems. Invariant Manifolds. The Phase Plane. Chaotic Dynamics. Bifurcation Theory. Hamiltonian Dynamics. Back Matter. Banner art adapted from a figure by Hinke M. Front Matter pp. Introduction pp.

Linear Systems pp. Existence and Uniqueness pp. Dynamical Systems pp. Invariant Manifolds pp. The Phase Plane pp.

Chaotic Dynamics pp. Bifurcation Theory pp. Hamiltonian Dynamics pp. Appendix pp. Back Matter pp.

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## Differential Dynamical Systems

This is a textbook on ordinary differential equations aimed at upper level undergraduates and beginning graduate students. Students are expected to have completed multivariable calculus and an introduction to analysis as prerequisites. Although it begins in a fairly traditional manner, the text gradually moves into a broader treatment of differential dynamical systems with an emphasis on understanding the qualitative behavior of these systems. The core of the book is the first six chapters. The first chapter introduces ordinary differential equations and the notion of a model, and offers several standard examples.

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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.

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We hope this content on epidemiology, disease modeling, pandemics and vaccines will help in the rapid fight against this global problem. Click on title above or here to access this collection. 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.