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Differential Equations: A Dynamical Systems Approach to Theory and Practice

Marcelo Viana IMPA - Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
In collaboration with Guilherme T. Goedert and Heber Mesa
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Softcover ISBN: 978-1-4704-6540-7
Product Code: GSM/212.S
List Price: $85.00 MAA Member Price:$76.50
AMS Member Price: $68.00 Electronic ISBN: 978-1-4704-6538-4 Product Code: GSM/212.E List Price:$85.00
MAA Member Price: $76.50 AMS Member Price:$68.00
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List Price: $127.50 MAA Member Price:$114.75
AMS Member Price: $102.00 Click above image for expanded view Differential Equations: A Dynamical Systems Approach to Theory and Practice Marcelo Viana IMPA - Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil José M. Espinar Universidad de Cádiz, Cadiz, Spain In collaboration with Guilherme T. Goedert and Heber Mesa Available Formats:  Softcover ISBN: 978-1-4704-6540-7 Product Code: GSM/212.S  List Price:$85.00 MAA Member Price: $76.50 AMS Member Price:$68.00
 Electronic ISBN: 978-1-4704-6538-4 Product Code: GSM/212.E
 List Price: $85.00 MAA Member Price:$76.50 AMS Member Price: $68.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$127.50 MAA Member Price: $114.75 AMS Member Price:$102.00
• Book Details

Volume: 2122021; 536 pp
MSC: Primary 34; Secondary 49; 65;

This graduate-level introduction to ordinary differential equations combines both qualitative and numerical analysis of solutions, in line with Poincaré's vision for the field over a century ago. Taking into account the remarkable development of dynamical systems since then, the authors present the core topics that every young mathematician of our time—pure and applied alike—ought to learn. The book features a dynamical perspective that drives the motivating questions, the style of exposition, and the arguments and proof techniques.

The text is organized in six cycles. The first cycle deals with the foundational questions of existence and uniqueness of solutions. The second introduces the basic tools, both theoretical and practical, for treating concrete problems. The third cycle presents autonomous and non-autonomous linear theory. Lyapunov stability theory forms the fourth cycle. The fifth one deals with the local theory, including the Grobman–Hartman theorem and the stable manifold theorem. The last cycle discusses global issues in the broader setting of differential equations on manifolds, culminating in the Poincaré–Hopf index theorem.

The book is appropriate for use in a course or for self-study. The reader is assumed to have a basic knowledge of general topology, linear algebra, and analysis at the undergraduate level. Each chapter ends with a computational experiment, a diverse list of exercises, and detailed historical, biographical, and bibliographic notes seeking to help the reader form a clearer view of how the ideas in this field unfolded over time.

• Chapters
• Introduction
• Local solutions
• Maximal solutions
• Numerical integration
• Autonomous equations
• Autonomous linear equations
• Non-autonomous linear equations
• Lyapunov stability
• Grobman–Hartman theorem
• Stable manifold theorem
• Vector fields on surfaces
• Poincaré–Hopf theorem
• Metric spaces and differentiable manifolds

• Reviews

• This book offers an attractive introduction to the modern theory of ordinary differential equations and dynamical systems at the graduate level. In many respects, the text creates a development of the subject in accordance with Poincaré's vision of more than a century ago. Of course, the field has evolved extensively since his time, but the emphasis on using a combination of qualitative analysis and numerical calculation of solutions remains very relevant. The authors succeed in coordinating both these elements to tell a pleasingly coherent and logical story.

Bill Satzer, University of Minnesota
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 2122021; 536 pp
MSC: Primary 34; Secondary 49; 65;

This graduate-level introduction to ordinary differential equations combines both qualitative and numerical analysis of solutions, in line with Poincaré's vision for the field over a century ago. Taking into account the remarkable development of dynamical systems since then, the authors present the core topics that every young mathematician of our time—pure and applied alike—ought to learn. The book features a dynamical perspective that drives the motivating questions, the style of exposition, and the arguments and proof techniques.

The text is organized in six cycles. The first cycle deals with the foundational questions of existence and uniqueness of solutions. The second introduces the basic tools, both theoretical and practical, for treating concrete problems. The third cycle presents autonomous and non-autonomous linear theory. Lyapunov stability theory forms the fourth cycle. The fifth one deals with the local theory, including the Grobman–Hartman theorem and the stable manifold theorem. The last cycle discusses global issues in the broader setting of differential equations on manifolds, culminating in the Poincaré–Hopf index theorem.

The book is appropriate for use in a course or for self-study. The reader is assumed to have a basic knowledge of general topology, linear algebra, and analysis at the undergraduate level. Each chapter ends with a computational experiment, a diverse list of exercises, and detailed historical, biographical, and bibliographic notes seeking to help the reader form a clearer view of how the ideas in this field unfolded over time.

• Chapters
• Introduction
• Local solutions
• Maximal solutions
• Numerical integration
• Autonomous equations
• Autonomous linear equations
• Non-autonomous linear equations
• Lyapunov stability
• Grobman–Hartman theorem
• Stable manifold theorem
• Vector fields on surfaces
• Poincaré–Hopf theorem
• Metric spaces and differentiable manifolds
• This book offers an attractive introduction to the modern theory of ordinary differential equations and dynamical systems at the graduate level. In many respects, the text creates a development of the subject in accordance with Poincaré's vision of more than a century ago. Of course, the field has evolved extensively since his time, but the emphasis on using a combination of qualitative analysis and numerical calculation of solutions remains very relevant. The authors succeed in coordinating both these elements to tell a pleasingly coherent and logical story.

Bill Satzer, University of Minnesota
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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