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Ordinary Differential Equations: Qualitative Theory
 
Luis Barreira Instituto Superior Técnico, Lisbon, Portugal
Claudia Valls Instituto Superior Técnico, Lisbon, Portugal
Ordinary Differential Equations
Softcover ISBN:  978-1-4704-7386-0
Product Code:  GSM/137.S
List Price: $68.00
MAA Member Price: $61.20
AMS Member Price: $54.40
eBook ISBN:  978-0-8218-8993-0
Product Code:  GSM/137.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7386-0
eBook: ISBN:  978-0-8218-8993-0
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
Ordinary Differential Equations
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Ordinary Differential Equations: Qualitative Theory
Luis Barreira Instituto Superior Técnico, Lisbon, Portugal
Claudia Valls Instituto Superior Técnico, Lisbon, Portugal
Softcover ISBN:  978-1-4704-7386-0
Product Code:  GSM/137.S
List Price: $68.00
MAA Member Price: $61.20
AMS Member Price: $54.40
eBook ISBN:  978-0-8218-8993-0
Product Code:  GSM/137.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7386-0
eBook ISBN:  978-0-8218-8993-0
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 Details
     
     
    Graduate Studies in Mathematics
    Volume: 1372012; 248 pp
    MSC: 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.

    Readership

    Undergraduate 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. Poincaré-Bendixson theory
    • Part 4. Further topics
    • Chapter 8. Bifurcations and center manifolds
    • Chapter 9. Hamiltonian systems
  • Requests
     
     
    Review Copy – for publishers of book reviews
    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: 1372012; 248 pp
MSC: 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.

Readership

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. Poincaré-Bendixson theory
  • Part 4. Further topics
  • Chapter 8. Bifurcations and center manifolds
  • Chapter 9. Hamiltonian systems
Review Copy – for publishers of book reviews
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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