| Softcover ISBN: | 978-1-4704-7641-0 |
| Product Code: | GSM/140.S |
| List Price: | $89.00 |
| MAA Member Price: | $80.10 |
| AMS Member Price: | $71.20 |
| eBook ISBN: | 978-0-8218-9104-9 |
| Product Code: | GSM/140.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Softcover ISBN: | 978-1-4704-7641-0 |
| eBook: ISBN: | 978-0-8218-9104-9 |
| Product Code: | GSM/140.S.B |
| List Price: | $174.00 $131.50 |
| MAA Member Price: | $156.60 $118.35 |
| AMS Member Price: | $139.20 $105.20 |
| Softcover ISBN: | 978-1-4704-7641-0 |
| Product Code: | GSM/140.S |
| List Price: | $89.00 |
| MAA Member Price: | $80.10 |
| AMS Member Price: | $71.20 |
| eBook ISBN: | 978-0-8218-9104-9 |
| Product Code: | GSM/140.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Softcover ISBN: | 978-1-4704-7641-0 |
| eBook ISBN: | 978-0-8218-9104-9 |
| Product Code: | GSM/140.S.B |
| List Price: | $174.00 $131.50 |
| MAA Member Price: | $156.60 $118.35 |
| AMS Member Price: | $139.20 $105.20 |
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Book DetailsGraduate Studies in MathematicsVolume: 140; 2012; 356 ppMSC: Primary 34; 37
This book provides a self-contained 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.
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Table of Contents
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Part 1. Classical theory
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Chapter 1. Introduction
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Chapter 2. Initial value problems
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Chapter 3. Linear equations
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Chapter 4. Differential equations in the complex domain
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Chapter 5. Boundary value problems
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Part 2. Dynamical systems
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Chapter 6. Dynamical systems
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Chapter 7. Planar dynamical systems
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Chapter 8. Higher dimensional dynamical systems
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Chapter 9. Local behavior near fixed points
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Part 3. Chaos
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Chapter 10. Discrete dynamical systems
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Chapter 11. Discrete dynamical systems in one dimension
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Chapter 12. Periodic solutions
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Chapter 13. Chaos in higher dimensional systems
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Additional Material
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Reviews
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It's easy to build all sorts of courses from this book — a classical one-semester course with a brief introduction to dynamical systems, a one-semester dynamical systems course with just brief coverage of the existence and linear systems theory, or a rather nice two-semester course based on most (if not all) of the material.
MAA Reviews
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseInstructor's Solutions Manual – for instructors who have adopted an AMS textbook for a courseExamination 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
- Additional Material
- Reviews
- Requests
This book provides a self-contained 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
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Chapter 7. Planar dynamical systems
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Chapter 8. Higher dimensional dynamical systems
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Chapter 9. Local behavior near fixed points
-
Part 3. Chaos
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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 one-semester course with a brief introduction to dynamical systems, a one-semester dynamical systems course with just brief coverage of the existence and linear systems theory, or a rather nice two-semester course based on most (if not all) of the material.
MAA Reviews
