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Graduate Studies in Mathematics
2006; 467 pp; hardcover
List Price: US$71
Member Price: US$56.80
Order Code: GSM/75
This book is a survey of asymptotic methods set in the current applied research context of wave propagation. It stresses rigorous analysis in addition to formal manipulations. Asymptotic expansions developed in the text are justified rigorously, and students are shown how to obtain solid error estimates for asymptotic formulae. The book relates examples and exercises to subjects of current research interest, such as the problem of locating the zeros of Taylor polynomials of entire nonvanishing functions and the problem of counting integer lattice points in subsets of the plane with various geometrical properties of the boundary.
The book is intended for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and applied mathematics as well as science and engineering. The basic prerequisite is a background in differential equations, linear algebra, advanced calculus, and complex variables at the level of introductory undergraduate courses on these subjects.
The book is ideally suited to the needs of a graduate student who, on the one hand, wants to learn basic applied mathematics, and on the other, wants to understand what is needed to make the various arguments rigorous. Down here in the Village, this is known as the Courant point of view!!
--Percy Deift, Courant Institute, New York
Peter D. Miller is an associate professor of mathematics at the University of Michigan at Ann Arbor. He earned a Ph.D. in Applied Mathematics from the University of Arizona and has held positions at the Australian National University (Canberra) and Monash University (Melbourne). His current research interests lie in singular limits for integrable systems.
Graduate students and research mathematicians interested in pure and applied mathematics and science and engineering.
"What is really special about the book is that it includes discussions on a number of topics that are usually not found in books on asymptotics ... very clear and student-friendly ... ideal textbook for a graduate course on asymptotic analysis. Highly recommended."
-- Arno Kuijlaars for Journal of Approximation Theory
"This manuscript will definitely have a big impact in showing that applied asymptotics analysis derives from classical analysis. Moreover, applications continue to demonstrate its continuing importance and vitality. Miller does an outstanding job of delivering this important message."
-- Robert O'Malley, University of Washington
"This book is very well-written, is mathematically very careful, and he has done a terrific job in explaining many of the subtle points in asymptotic analysis ... the quality is certainly first rate. ... His pedagogy is excellent."
-- Michael Ward, University of British Columbia
"This book combines some of the best information available to graduate students on asymptotics...Miller seems to add lots of motivation and careful explanations, certainly indicating that he was a top students and that he is a good teacher. ... In summary, this new book brings one to the frontier of much current research, both pure and applied. ... I recommend it highly."
-- SIAM Review
"Peter Miller's book is an ideal textbook for a graduate course on asymptotic analysis. Highly recommended."
-- Journal of Approximation Theory
"The text is self-contained and the exposition is well-written. ... (It) is accompanied by a considerable number of well-chosen examples and exercises that illustrate the theory."
-- European Mathematical Society Newsletter
"The book is a very good survey of asymptotic methods. Besides the constructions of formal approximations it also gives rigorous proofs of their validity in most cases. There are many useful examples and exercises. The clarity of exposition makes it a very suitable textbook."
-- Mathematical Reviews
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