Softcover ISBN:  9781470473860 
Product Code:  GSM/137.S 
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AMS Member Price:  $54.40 
eBook ISBN:  9780821889930 
Product Code:  GSM/137.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470473860 
eBook: ISBN:  9780821889930 
Product Code:  GSM/137.S.B 
List Price:  $153.00 $110.50 
MAA Member Price:  $137.70 $99.45 
AMS Member Price:  $122.40 $88.40 
Softcover ISBN:  9781470473860 
Product Code:  GSM/137.S 
List Price:  $68.00 
MAA Member Price:  $61.20 
AMS Member Price:  $54.40 
eBook ISBN:  9780821889930 
Product Code:  GSM/137.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470473860 
eBook ISBN:  9780821889930 
Product Code:  GSM/137.S.B 
List Price:  $153.00 $110.50 
MAA Member Price:  $137.70 $99.45 
AMS Member Price:  $122.40 $88.40 

Book DetailsGraduate Studies in MathematicsVolume: 137; 2012; 248 ppMSC: Primary 34; 37
This textbook provides a comprehensive introduction to the qualitative theory of ordinary differential equations. It includes a discussion of the existence and uniqueness of solutions, phase portraits, linear equations, stability theory, hyperbolicity and equations in the plane. The emphasis is primarily on results and methods that allow one to analyze qualitative properties of the solutions without solving the equations explicitly. The text includes numerous examples that illustrate in detail the new concepts and results as well as exercises at the end of each chapter. The book is also intended to serve as a bridge to important topics that are often left out of a course on ordinary differential equations. In particular, it provides brief introductions to bifurcation theory, center manifolds, normal forms and Hamiltonian systems.
ReadershipUndergraduate and graduate students interested in ordinary differential equations, dynamical systems, bifurcation theory, and Hamiltonian systems.

Table of Contents

Part 1. Basic concepts and linear equations

Chapter 1. Ordinary differential equations

Chapter 2. Linear equations and conjugacies

Part 2. Stability of hyperbolicity

Chapter 3. Stability and Lyapunov functions

Chapter 4. Hyperbolicity and topological conjugacies

Chapter 5. Existence of invariant manifolds

Part 3. Equations in the plane

Chapter 6. Index theory

Chapter 7. PoincaréBendixson theory

Part 4. Further topics

Chapter 8. Bifurcations and center manifolds

Chapter 9. Hamiltonian systems


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This textbook provides a comprehensive introduction to the qualitative theory of ordinary differential equations. It includes a discussion of the existence and uniqueness of solutions, phase portraits, linear equations, stability theory, hyperbolicity and equations in the plane. The emphasis is primarily on results and methods that allow one to analyze qualitative properties of the solutions without solving the equations explicitly. The text includes numerous examples that illustrate in detail the new concepts and results as well as exercises at the end of each chapter. The book is also intended to serve as a bridge to important topics that are often left out of a course on ordinary differential equations. In particular, it provides brief introductions to bifurcation theory, center manifolds, normal forms and Hamiltonian systems.
Undergraduate and graduate students interested in ordinary differential equations, dynamical systems, bifurcation theory, and Hamiltonian systems.

Part 1. Basic concepts and linear equations

Chapter 1. Ordinary differential equations

Chapter 2. Linear equations and conjugacies

Part 2. Stability of hyperbolicity

Chapter 3. Stability and Lyapunov functions

Chapter 4. Hyperbolicity and topological conjugacies

Chapter 5. Existence of invariant manifolds

Part 3. Equations in the plane

Chapter 6. Index theory

Chapter 7. PoincaréBendixson theory

Part 4. Further topics

Chapter 8. Bifurcations and center manifolds

Chapter 9. Hamiltonian systems