Ohio State University, Columbus, USA University of Newcastle upon Tyne, UK Centre National de La Recherche Scientifique/College of Fran Texas A & M University

"…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

• Introduction. Review of Some Basic Tools. Classical Asymptotics. Analyzable Functions and Transseries. Borel Summability in Differential Equations. Asymptotic and Transasymptotic Matching; Formation of Singularities. Other Classes of Problems. Other Important Tools and Developments. References. Index.

Ohio State University, Columbus, USA University of Newcastle upon Tyne, UK Centre National de La Recherche Scientifique/College of Fran Texas A & M University

"…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

• Introduction. Review of Some Basic Tools. Classical Asymptotics. Analyzable Functions and Transseries. Borel Summability in Differential Equations. Asymptotic and Transasymptotic Matching; Formation of Singularities. Other Classes of Problems. Other Important Tools and Developments. References. Index.

Ohio State University, Columbus, USA University of Newcastle upon Tyne, UK Centre National de La Recherche Scientifique/College of Fran Texas A & M University

"…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

• Introduction. Review of Some Basic Tools. Classical Asymptotics. Analyzable Functions and Transseries. Borel Summability in Differential Equations. Asymptotic and Transasymptotic Matching; Formation of Singularities. Other Classes of Problems. Other Important Tools and Developments. References. Index.