A Distributional Approach to Asymptotics : Theory and Appications (Birkhäuser Advanced Texts / Basler Lehrbücher)
by: Ricardo Estrada and Ram P. Kanwal
Details
# Hardcover: 480 pages
# Publisher: Birkhäuser Boston; 2nd edition (February 8, 2002)
# Language: English
# ISBN-10: 0817641424
# ISBN-13: 978-0817641429
Description
This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory.
Key features of this significantly expanded second edition: - addition of several new chapters and sections, including a presentation of time-domain asymptotics needed for the understanding of wavelet theory - extensive examples and problem sets - useful bibliography and index.
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Asymptotics and Borel Summability (Chapman & Hall/Crc Monographs and Surveys in Pure and Applied Mathematics)
by: Ovidiu Costin
Details
# Hardcover: 256 pages
# Publisher: Chapman & Hall/CRC; 1 edition (December 4, 2008)
# Language: English
# ISBN-10: 1420070312
# ISBN-13: 978-1420070316
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.
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Algebraic Analysis of Differential Equations: from Microlocal Analysis to Exponential Asymptotics
by: T. Aoki, H. Majima, Y. Takei, N. Tose
Details
# Hardcover: 352 pages
# Publisher: Springer; 1 edition (November 16, 2007)
# Language: English
# ISBN-10: 443173239X
# ISBN-13: 978-4431732396
Description
This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the international conference "Algebraic Analysis of Differential Equations – from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005. Microlocal analysis and exponential asymptotics are intimately connected and provide powerful tools that have been applied to linear and non-linear differential equations as well as many related fields such as real and complex analysis, integral transforms, spectral theory, inverse problems, integrable systems, and mathematical physics. The articles contained here present many new results and ideas, providing interested researchers and students with valuable suggestions and instructive guidance for their work. This volume is dedicated to Professor Takahiro Kawai, who is one of the creators of microlocal analysis and who introduced the technique of microlocal analysis into exponential asymptotics. This dedication is made on the occasion of Professor Kawai's 60th birthday as a token of deep appreciation of the important contributions he has made to the field. Introductory notes on the scientific works of Professor Kawai are also included.
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