| Asymptotics and Borel Summability Contributor(s): Costin, Ovidiu (Author) |
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ISBN: 1420070312 ISBN-13: 9781420070316 Publisher: CRC Press OUR PRICE: $190.00 Product Type: Hardcover - Other Formats Published: June 2008 Annotation: Providing a complete treatment of asymptotics, including exponential asymptotics and generalized Borel summability, Asymptotics and Borel Summability provides a rigorous theoretical basis while also exploring applications to various problems in ordinary and partial differential equations and difference equations. The book includes exercises making it suitable for self-study and a second course in asymptotic theory. It also includes open problems for future research. The book is intended for pure and applied mathematicians, as well as physicists and engineers interested in asymptotics and perturbation methods. |
| Additional Information |
| BISAC Categories: - Mathematics | Differential Equations - General - Mathematics | Applied |
| Dewey: 515.35 |
| LCCN: 2008034107 |
| Series: Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Math |
| Physical Information: 0.9" H x 6.2" W x 9.3" (1.30 lbs) 256 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, transseries, and exponential asymptotics. He provides complete mathematical rigor while supplementing it with heuristic material and examples, so that some proofs may be omitted by applications-oriented readers. To give a sense of how new methods are used in a systematic way, the book analyzes in detail general nonlinear ordinary differential equations (ODEs) near a generic irregular singular point. It enables readers to master basic techniques, supplying a firm foundation for further study at more advanced levels. The book also examines difference equations, partial differential equations (PDEs), and other types of problems. Chronicling the progress made in recent decades, this book shows how Borel summability can recover exact solutions from formal expansions, analyze singular behavior, and vastly improve accuracy in asymptotic approximations. |