Asymptotics and Borel Summability (Monographs and Surveys in Pure and Applied Mathematics) 1st Edition by Ovidiu Costin (PDF)

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.

User’s Reviews

Editorial Reviews: Review “…Until the welcome publication of Ovidiu Costin’s textbook on the subject, this more modern approach to asymptotic analysis was only accessible via original research papers and a few technical lecture note publications. …the author’s perspective provides some key new insights not found in [traditional] books. …One of the great strengths of this book is its use of many examples to illustrate general theory. … A good first course on the subject of transseries and Borel summation could be designed around these examples. …The author maintains a comprehensive list of corrections organized by page number on the web … In summary, as one of a small number of experts in the subject of transseries and Borel summation, Ovidiu Costin has written a book that will be a fundamental reference to researchers and students interested in going beyond the standard classical methods of asymptotic analysis.”―Journal of Approximation Theory, 2010″This important new book is about asymptotics beyond all orders, i.e., recovering actual solutions from formal expansions. The book goes far beyond the logarithmico-exponentials of Hardy and the Borel–Ritt theory of Wasow by utilizing recent work of Ecalle and Costin, among others. … This unique monograph should stimulate a broad new effort to demystify the use of asymptotic series.”―SIAM Review, Volume 51, Issue 3, 2009

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐

⭐

Keywords

Free Download Asymptotics and Borel Summability (Monographs and Surveys in Pure and Applied Mathematics) 1st Edition in PDF format
Asymptotics and Borel Summability (Monographs and Surveys in Pure and Applied Mathematics) 1st Edition PDF Free Download
Download Asymptotics and Borel Summability (Monographs and Surveys in Pure and Applied Mathematics) 1st Edition 2008 PDF Free
Asymptotics and Borel Summability (Monographs and Surveys in Pure and Applied Mathematics) 1st Edition 2008 PDF Free Download
Download Asymptotics and Borel Summability (Monographs and Surveys in Pure and Applied Mathematics) 1st Edition PDF
Free Download Ebook Asymptotics and Borel Summability (Monographs and Surveys in Pure and Applied Mathematics) 1st Edition