Save up to xx% on snacks for your team
Ships from
Amazon.com
Amazon.com
Ships from
Amazon.com
Sold by
Amazon.com
Amazon.com
Sold by
Amazon.com
Returns
FREE 30-day refund/replacement
FREE 30-day refund/replacement
This item can be returned in its original condition for a full refund or replacement within 30 days of receipt.
Read full return policy
Payment
Secure transaction
Your transaction is secure
We work hard to protect your security and privacy. Our payment security system encrypts your information during transmission. We don’t share your credit card details with third-party sellers, and we don’t sell your information to others. Learn more
Kindle app logo image

Download the free Kindle app and start reading Kindle books instantly on your smartphone, tablet, or computer - no Kindle device required.

Read instantly on your browser with Kindle for Web.

Using your mobile phone camera - scan the code below and download the Kindle app.

QR code to download the Kindle App

Follow the author

Something went wrong. Please try your request again later.

Asymptotics and Borel Summability (Monographs and Surveys in Pure and Applied Mathematics) 1st Edition


Purchase options and add-ons

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.

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

About the Author

Ovidiu Costin

Product details

About the author

Follow authors to get new release updates, plus improved recommendations.
O. Costin
Brief content visible, double tap to read full content.
Full content visible, double tap to read brief content.

Discover more of the author’s books, see similar authors, read book recommendations and more.