Softcover ISBN:  9781470465407 
Product Code:  GSM/212.S 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Electronic ISBN:  9781470465384 
Product Code:  GSM/212.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 

Book DetailsGraduate Studies in MathematicsVolume: 212; 2021; 536 ppMSC: Primary 34; Secondary 49; 65;
This graduatelevel 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 nonautonomous 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 selfstudy. 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.ReadershipUndergraduate and graduate students interested in differential equations and dynamical systems.

Table of Contents

Chapters

Introduction

Local solutions

Maximal solutions

Numerical integration

Autonomous equations

Autonomous linear equations

Nonautonomous linear equations

Lyapunov stability

Grobman–Hartman theorem

Stable manifold theorem

Vector fields on surfaces

Poincaré–Hopf theorem

Metric spaces and differentiable manifolds


Additional Material

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


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This graduatelevel 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 nonautonomous 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 selfstudy. 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.
Undergraduate and graduate students interested in differential equations and dynamical systems.

Chapters

Introduction

Local solutions

Maximal solutions

Numerical integration

Autonomous equations

Autonomous linear equations

Nonautonomous 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