Hardcover ISBN:  9780821883280 
Product Code:  GSM/140 
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AMS Member Price:  $79.20 
eBook ISBN:  9780821891049 
Product Code:  GSM/140.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821883280 
eBook: ISBN:  9780821891049 
Product Code:  GSM/140.B 
List Price:  $184.00$141.50 
MAA Member Price:  $165.60$127.35 
AMS Member Price:  $147.20$113.20 
Hardcover ISBN:  9780821883280 
Product Code:  GSM/140 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9780821891049 
Product Code:  GSM/140.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821883280 
eBook ISBN:  9780821891049 
Product Code:  GSM/140.B 
List Price:  $184.00$141.50 
MAA Member Price:  $165.60$127.35 
AMS Member Price:  $147.20$113.20 

Book DetailsGraduate Studies in MathematicsVolume: 140; 2012; 356 ppMSC: Primary 34; 37;
This book provides a selfcontained 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.
Ancillaries:ReadershipGraduate students interested in ordinary differential equations and dynamical systems.

Table of Contents

Part 1. Classical theory

Chapter 1. Introduction

Chapter 2. Initial value problems

Chapter 3. Linear equations

Chapter 4. Differential equations in the complex domain

Chapter 5. Boundary value problems

Part 2. Dynamical systems

Chapter 6. Dynamical systems

Chapter 7. Planar dynamical systems

Chapter 8. Higher dimensional dynamical systems

Chapter 9. Local behavior near fixed points

Part 3. Chaos

Chapter 10. Discrete dynamical systems

Chapter 11. Discrete dynamical systems in one dimension

Chapter 12. Periodic solutions

Chapter 13. Chaos in higher dimensional systems


Additional Material

Reviews

It's easy to build all sorts of courses from this book — a classical onesemester course with a brief introduction to dynamical systems, a onesemester dynamical systems course with just brief coverage of the existence and linear systems theory, or a rather nice twosemester course based on most (if not all) of the material.
MAA Reviews


RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseInstructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manualExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
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This book provides a selfcontained 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.
Ancillaries:
Graduate students interested in ordinary differential equations and dynamical systems.

Part 1. Classical theory

Chapter 1. Introduction

Chapter 2. Initial value problems

Chapter 3. Linear equations

Chapter 4. Differential equations in the complex domain

Chapter 5. Boundary value problems

Part 2. Dynamical systems

Chapter 6. Dynamical systems

Chapter 7. Planar dynamical systems

Chapter 8. Higher dimensional dynamical systems

Chapter 9. Local behavior near fixed points

Part 3. Chaos

Chapter 10. Discrete dynamical systems

Chapter 11. Discrete dynamical systems in one dimension

Chapter 12. Periodic solutions

Chapter 13. Chaos in higher dimensional systems

It's easy to build all sorts of courses from this book — a classical onesemester course with a brief introduction to dynamical systems, a onesemester dynamical systems course with just brief coverage of the existence and linear systems theory, or a rather nice twosemester course based on most (if not all) of the material.
MAA Reviews