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Selected Topics in the Geometrical Study of Differential Equations

Niky Kamran McGill University, Montreal, QC, Canada
A co-publication of the AMS and CBMS
Available Formats:
Softcover ISBN: 978-0-8218-2639-3
Product Code: CBMS/96
List Price: $32.00 Individual Price:$25.60
Electronic ISBN: 978-1-4704-2456-5
Product Code: CBMS/96.E
List Price: $30.00 Individual Price:$24.00
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List Price: $48.00 Click above image for expanded view Selected Topics in the Geometrical Study of Differential Equations Niky Kamran McGill University, Montreal, QC, Canada A co-publication of the AMS and CBMS Available Formats:  Softcover ISBN: 978-0-8218-2639-3 Product Code: CBMS/96  List Price:$32.00 Individual Price: $25.60  Electronic ISBN: 978-1-4704-2456-5 Product Code: CBMS/96.E  List Price:$30.00 Individual Price: $24.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$48.00
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 962002; 115 pp
MSC: Primary 58; 35;

The geometrical study of differential equations has a long and distinguished history, dating back to the classical investigations of Sophus Lie, Gaston Darboux, and Elie Cartan. Currently, these ideas occupy a central position in several areas of pure and applied mathematics, including the theory of completely integrable evolution equations, the calculus of variations, and the study of conservation laws. In this book, the author gives an overview of a number of significant ideas and results developed over the past decade in the geometrical study of differential equations.

Topics covered in the book include symmetries of differential equations and variational problems, the variational bi-complex and conservation laws, geometric integrability for hyperbolic equations, transformations of submanifolds and systems of conservation laws, and an introduction to the characteristic cohomology of differential systems.

The exposition is sufficiently elementary so that non-experts can understand the main ideas and results by working independently. The book is also suitable for graduate students and researchers interested in the study of differential equations from a geometric perspective. It can serve nicely as a companion volume to The Geometrical Study of Differential Equations, Volume 285 in the AMS series, Contemporary Mathematics.

Graduate students and research mathematicians interested in the study of differential equations from a geometric perspective.

• Chapters
• Chapter 1. Differential equations and their geometry
• Chapter 2. External and generalized symmetries
• Chapter 3. Internal, external and generalized symmetries
• Chapter 4. Transformations of surfaces
• Chapter 5. Tranformations of submanifolds
• Chapter 6. Hamiltonian systems of conservation laws
• Chapter 7. The variational bi-complex
• Chapter 8. The inverse problem of the calculus of variations
• Chapter 9. Conservation laws and Darboux integrability
• Chapter 10. Characteristic cohomology of differential systems
• Reviews

• The author performs an outstanding feat of concise exposition … exposition is concise yet informative … the author does a wonderful job in conveying, in a little over 100 pages, some sense of the subject's diversity of ideas and results … written in a clear and lucid style and is recommended as a fine introduction to the geometry of differential equations.

Mathematical Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 962002; 115 pp
MSC: Primary 58; 35;

The geometrical study of differential equations has a long and distinguished history, dating back to the classical investigations of Sophus Lie, Gaston Darboux, and Elie Cartan. Currently, these ideas occupy a central position in several areas of pure and applied mathematics, including the theory of completely integrable evolution equations, the calculus of variations, and the study of conservation laws. In this book, the author gives an overview of a number of significant ideas and results developed over the past decade in the geometrical study of differential equations.

Topics covered in the book include symmetries of differential equations and variational problems, the variational bi-complex and conservation laws, geometric integrability for hyperbolic equations, transformations of submanifolds and systems of conservation laws, and an introduction to the characteristic cohomology of differential systems.

The exposition is sufficiently elementary so that non-experts can understand the main ideas and results by working independently. The book is also suitable for graduate students and researchers interested in the study of differential equations from a geometric perspective. It can serve nicely as a companion volume to The Geometrical Study of Differential Equations, Volume 285 in the AMS series, Contemporary Mathematics.

Graduate students and research mathematicians interested in the study of differential equations from a geometric perspective.

• Chapters
• Chapter 1. Differential equations and their geometry
• Chapter 2. External and generalized symmetries
• Chapter 3. Internal, external and generalized symmetries
• Chapter 4. Transformations of surfaces
• Chapter 5. Tranformations of submanifolds
• Chapter 6. Hamiltonian systems of conservation laws
• Chapter 7. The variational bi-complex
• Chapter 8. The inverse problem of the calculus of variations
• Chapter 9. Conservation laws and Darboux integrability
• Chapter 10. Characteristic cohomology of differential systems
• The author performs an outstanding feat of concise exposition … exposition is concise yet informative … the author does a wonderful job in conveying, in a little over 100 pages, some sense of the subject's diversity of ideas and results … written in a clear and lucid style and is recommended as a fine introduction to the geometry of differential equations.

Mathematical Reviews
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.